1
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Duh M, Gosak M, Perc M. Mixing protocols in the public goods game. Phys Rev E 2020; 102:032310. [PMID: 33076040 DOI: 10.1103/physreve.102.032310] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 09/10/2020] [Indexed: 11/07/2022]
Abstract
If interaction partners in social dilemma games are not selected randomly from the population but are instead determined by a network of contacts, it has far reaching consequences for the evolutionary dynamics. Selecting partners randomly leads to a well-mixed population, where pattern formation is essentially impossible. This rules out important mechanisms that can facilitate cooperation, most notably network reciprocity. In contrast, if interactions are determined by a lattice or a network, then the population is said to be structured, where cooperators can form compact clusters that protect them from invading defectors. Between these two extremes, however, there is ample middle ground that can be brought about by the consideration of temporal networks, mobility, or other coevolutionary processes. The question that we here seek to answer is, when does mixing on a lattice actually lead to well-mixed conditions? To that effect, we use the public goods game on a square lattice, and we consider nearest-neighbor and random mixing with different frequencies, as well as a mix of both mixing protocols. Not surprisingly, we find that nearest-neighbor mixing requires a higher frequency than random mixing to arrive at the well-mixed limit. The differences between the two mixing protocols are most expressed at intermediate mixing frequencies, whilst at very low and very high mixing frequencies the two almost converge. We also find a near universal exponential growth of the average size of cooperator clusters as their fraction increases from zero to one, regardless of whether this increase is due to increasing the multiplication factor of the public goods, decreasing the frequency of mixing, or gradually shifting the mixing from random to nearest neighbors.
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Affiliation(s)
- Maja Duh
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
| | - Marko Gosak
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia.,Faculty of Medicine, University of Maribor, Taborska ulica 8, 2000 Maribor, Slovenia
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia.,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.,Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
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2
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Abstract
Trust and trustworthiness form the basis for continued social and economic interactions, and they are also fundamental for cooperation, fairness, honesty, and indeed for many other forms of prosocial and moral behaviour. However, trust entails risks, and building a trustworthy reputation requires effort. So how did trust and trustworthiness evolve, and under which conditions do they thrive? To find answers, we operationalize trust and trustworthiness using the trust game with the trustor's investment and the trustee's return of the investment as the two key parameters. We study this game on different networks, including the complete network, random and scale-free networks, and in the well-mixed limit. We show that in all but one case, the network structure has little effect on the evolution of trust and trustworthiness. Specifically, for well-mixed populations, lattices, random and scale-free networks, we find that trust never evolves, while trustworthiness evolves with some probability depending on the game parameters and the updating dynamics. Only for the scale-free network with degree non-normalized dynamics, we find parameter values for which trust evolves but trustworthiness does not, as well as values for which both trust and trustworthiness evolve. We conclude with a discussion about mechanisms that could lead to the evolution of trust and outline directions for future work.
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Affiliation(s)
- Aanjaneya Kumar
- Department of Physics, Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India
| | - Valerio Capraro
- Department of Economics, Middlesex University, The Burroughs, London NW4 4BT, UK
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia.,Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan.,Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
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3
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Capraro V, Perc M, Vilone D. Lying on networks: The role of structure and topology in promoting honesty. Phys Rev E 2020; 101:032305. [PMID: 32289998 DOI: 10.1103/physreve.101.032305] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2019] [Accepted: 02/24/2020] [Indexed: 06/11/2023]
Abstract
Lies can have a negating impact on governments, companies, and the society as a whole. Understanding the dynamics of lying is therefore of crucial importance across different fields of research. While lying has been studied before in well-mixed populations, it is a fact that real interactions are rarely well-mixed. Indeed, they are usually structured and thus best described by networks. Here we therefore use the Monte Carlo method to study the evolution of lying in the sender-receiver game in a one-parameter family of networks, systematically covering complete networks, small-world networks, and one-dimensional rings. We show that lies that benefit the sender at a cost to the receiver, the so-called black lies, are less likely to proliferate on networks than they do in well-mixed populations. Honesty is thus more likely to evolve, but only when the benefit for the sender is smaller than the cost for the receiver. Moreover, this effect is particularly strong in small-world networks, but less so in the one-dimensional ring. For lies that favor the receiver at a cost to the sender, the so-called altruistic white lies, we show that honesty is also more likely to evolve than it is in well-mixed populations. But contrary to black lies, this effect is more expressed in the one-dimensional ring, whereas in small-world networks it is present only when the cost to the sender is greater than the benefit for the receiver. Last, for lies that benefit both the sender and the receiver, the so-called Pareto white lies, we show that the network structure actually favors the evolution of lying, but this only occurs when the benefit for the sender is slightly greater than the benefit for the receiver. In this case again the small-world topology acts as an amplifier of the effect, while other network topologies fail to do the same. In addition to these main results we discuss several other findings, which together show clearly that the structure of interactions and the overall topology of the network critically determine the dynamics of lying.
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Affiliation(s)
- Valerio Capraro
- Department of Economics, Middlesex University, The Burroughs, London NW4 4BT, United Kingdom
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan
- Complexity Science Hub Vienna, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Daniele Vilone
- Laboratory of Agent Based Social Simulation, Institute of Cognitive Science and Technology, National Research Council, Via Palestro 32, 00185 Rome, Italy
- Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
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4
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Rong Z, Wu ZX, Li X, Holme P, Chen G. Heterogeneous cooperative leadership structure emerging from random regular graphs. CHAOS (WOODBURY, N.Y.) 2019; 29:103103. [PMID: 31675848 DOI: 10.1063/1.5120349] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2019] [Accepted: 09/10/2019] [Indexed: 06/10/2023]
Abstract
This paper investigates the evolution of cooperation and the emergence of hierarchical leadership structure in random regular graphs. It is found that there exist different learning patterns between cooperators and defectors, and cooperators are able to attract more followers and hence more likely to become leaders. Hence, the heterogeneous distributions of reputation and leadership can emerge from homogeneous random graphs. The important directed game-learning skeleton is then studied, revealing some important structural properties, such as the heavy-tailed degree distribution and the positive in-in degree correlation.
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Affiliation(s)
- Zhihai Rong
- School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
| | - Zhi-Xi Wu
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou 730000, China
| | - Xiang Li
- Adaptive Networks and Control Lab, Department of Electronic Engineering, Fudan University, Shanghai 200433, China
| | - Petter Holme
- Tokyo Tech World Research Hub Initiative (WRHI), Institute of Innovative Research, Tokyo Institute of Technology, Nagatsuta-cho 4259, Midori-ku, Yokohama, Kanagawa 226-8503, Japan
| | - Guanrong Chen
- Department of Electrical Engineering, City University of Hong Kong, Hong Kong, China
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5
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Geng Y, Hu K, Shen C, Shi L, Wang Z. Aspiration induced interdependence leads to optimal cooperation level. CHAOS (WOODBURY, N.Y.) 2019; 29:083114. [PMID: 31472494 DOI: 10.1063/1.5093014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2019] [Accepted: 07/24/2019] [Indexed: 06/10/2023]
Abstract
How to couple different networks is a key issue in interdependent networks, where information sharing and payoff coupling are two frequently used methods. Unlike previous studies, in this paper, we propose a new coupling mode and test its performance in interdependent networks. Specifically, a player tends to seek additional support on another network only if his environment (defined as the proportion of holding different strategies in the neighborhood) is worse enough and exceeds an aspiration level. Conversely, it turns to the traditional version on single network if his environment is pleasing enough (the value of environment is small). Whether to establish additional support will directly influence the range of selecting fittest learning objects. As we can see from numerical results, moderate aspiration introduces diversity into the system and cooperation evolves with the support of network coupling. Besides, we also demonstrate that players with external links on the boundary of cooperative clusters protect internal cooperators and attract more players to cooperate under preferential selection rule.
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Affiliation(s)
- Yini Geng
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Kaipeng Hu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Chen Shen
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China
| | - Zhen Wang
- School of Mechanical Engineering and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an 710072, China
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6
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Identification of influential invaders in evolutionary populations. Sci Rep 2019; 9:7305. [PMID: 31086258 PMCID: PMC6514010 DOI: 10.1038/s41598-019-43853-9] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Accepted: 05/01/2019] [Indexed: 11/08/2022] Open
Abstract
The identification of the most influential nodes has been a vibrant subject of research across the whole of network science. Here we map this problem to structured evolutionary populations, where strategies and the interaction network are both subject to change over time based on social inheritance. We study cooperative communities, which cheaters can invade because they avoid the cost of contributions that are associated with cooperation. The question that we seek to answer is at which nodes cheaters invade most successfully. We propose the weighted degree decomposition to identify and rank the most influential invaders. More specifically, we distinguish two kinds of ranking based on the weighted degree decomposition. We show that a ranking strategy based on negative-weighted degree allows to successfully identify the most influential invaders in the case of weak selection, while a ranking strategy based on positive-weighted degree performs better when the selection is strong. Our research thus reveals how to identify the most influential invaders based on statistical measures in dynamically evolving cooperative communities.
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7
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Shen C, Chu C, Shi L, Jusup M, Perc M, Wang Z. Coevolutionary resolution of the public goods dilemma in interdependent structured populations. ACTA ACUST UNITED AC 2018. [DOI: 10.1209/0295-5075/124/48003] [Citation(s) in RCA: 50] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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8
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Verma P, Nandi AK, Sengupta S. Bribery games on interdependent complex networks. J Theor Biol 2018; 450:43-52. [PMID: 29704488 DOI: 10.1016/j.jtbi.2018.04.028] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2017] [Revised: 04/18/2018] [Accepted: 04/19/2018] [Indexed: 11/16/2022]
Abstract
Bribe demands present a social conflict scenario where decisions have wide-ranging economic and ethical consequences. Nevertheless, such incidents occur daily in many countries across the globe. Harassment bribery constitute a significant sub-set of such bribery incidents where a government official demands a bribe for providing a service to a citizen legally entitled to it. We employ an evolutionary game-theoretic framework to analyse the evolution of corrupt and honest strategies in structured populations characterized by an interdependent complex network. The effects of changing network topology, average number of links and asymmetry in size of the citizen and officer population on the proliferation of incidents of bribery are explored. A complex network topology is found to be beneficial for the dominance of corrupt strategies over a larger region of phase space when compared with the outcome for a regular network, for equal citizen and officer population sizes. However, the extent of the advantage depends critically on the network degree and topology. A different trend is observed when there is a difference between the citizen and officer population sizes. Under those circumstances, increasing randomness of the underlying citizen network can be beneficial to the fixation of honest officers up to a certain value of the network degree. Our analysis reveals how the interplay between network topology, connectivity and strategy update rules can affect population level outcomes in such asymmetric games.
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Affiliation(s)
- Prateek Verma
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, India
| | - Anjan K Nandi
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, India
| | - Supratim Sengupta
- Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, India.
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9
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Abstract
The question of why and how animal and human groups form temporarily stable hierarchical organizations has long been a great challenge from the point of quantitative interpretations. The prevailing observation/consensus is that a hierarchical social or technological structure is optimal considering a variety of aspects. Here we introduce a simple quantitative interpretation of this situation using a statistical mechanics-type approach. We look for the optimum of the efficiency function \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${E}_{eff}=1/N{\sum }_{ij}{J}_{ij}{a}_{i}{a}_{j}$$\end{document}Eeff=1/N∑ijJijaiaj with Jij denoting the nature of the interaction between the units i and j and ai standing for the ability of member i to contribute to the efficiency of the system. Notably, this expression for Eeff has a similar structure to that of the energy as defined for spin-glasses. Unconventionally, we assume that Jij-s can have the values 0 (no interaction), +1 and −1; furthermore, a direction is associated with each edge. The essential and novel feature of our approach is that instead of optimizing the state of the nodes of a pre-defined network, we search for extrema for given ai-s in the complex efficiency landscape by finding locally optimal network topologies for a given number of edges of the subgraphs considered.
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10
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Amaral MA, Perc M, Wardil L, Szolnoki A, da Silva Júnior EJ, da Silva JKL. Role-separating ordering in social dilemmas controlled by topological frustration. Phys Rev E 2017; 95:032307. [PMID: 28415219 DOI: 10.1103/physreve.95.032307] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2016] [Indexed: 06/07/2023]
Abstract
''Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.
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Affiliation(s)
- Marco A Amaral
- Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30161-970, Belo Horizonte-MG, Brazil
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
- CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia
| | - Lucas Wardil
- Departamento de Fisica, Universidade Federal de Ouro Preto, Ouro Preto, MG, Brazil
| | - Attila Szolnoki
- Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences, Post Office Box 49, H-1525 Budapest, Hungary
| | - Elton J da Silva Júnior
- Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30161-970, Belo Horizonte-MG, Brazil
| | - Jafferson K L da Silva
- Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30161-970, Belo Horizonte-MG, Brazil
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11
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Abstract
Many evolutionary game models for network reciprocity are based on an imitation dynamics, yet how semirational imitators prevail has seldom been explained. Here we use a model to investigate the coevolutionary dynamics of cooperation and partnership adjustment in a polygenic population of semirational imitators and rational payoff maximizers. A rational individual chooses a strategy best responding to its neighbors when updating strategy and switches to a new partner who can bring it the maximal payoff from all candidates when adjusting the partnership. In contrast, a semirational individual imitates its neighbor's strategy directly and adjusts its partnership based upon a simple reputation rule. Individual-based simulations show that cooperation cannot evolve in a population of all best responders even if they can switch their partners to somebody who can reward them best in game playing. However, when imitators exist, a stable community that consists of cooperative imitators emerges. Further, we show that a birth-death selection mechanism can eliminate all best responders, cultivating a social regime of all cooperative imitators. Compared with parallel simulations that assume fixed networks, cooperative imitators are evolutionarily favored, provided they are able to adjust their partners.
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Affiliation(s)
- Yixiao Li
- Department of Information Management, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang, People's Republic of China
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12
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Aleta A, Meloni S, Perc M, Moreno Y. From degree-correlated to payoff-correlated activity for an optimal resolution of social dilemmas. Phys Rev E 2016; 94:062315. [PMID: 28085417 DOI: 10.1103/physreve.94.062315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2016] [Indexed: 06/06/2023]
Abstract
An active participation of players in evolutionary games depends on several factors, ranging from personal stakes to the properties of the interaction network. Diverse activity patterns thus have to be taken into account when studying the evolution of cooperation in social dilemmas. Here we study the weak prisoner's dilemma game, where the activity of each player is determined in a probabilistic manner either by its degree or by its payoff. While degree-correlated activity introduces cascading failures of cooperation that are particularly severe on scale-free networks with frequently inactive hubs, payoff-correlated activity provides a more nuanced activity profile, which ultimately hinders systemic breakdowns of cooperation. To determine optimal conditions for the evolution of cooperation, we introduce an exponential decay to payoff-correlated activity that determines how fast the activity of a player returns to its default state. We show that there exists an intermediate decay rate at which the resolution of the social dilemma is optimal. This can be explained by the emerging activity patterns of players, where the inactivity of hubs is compensated effectively by the increased activity of average-degree players, who through their collective influence in the network sustain a higher level of cooperation. The sudden drops in the fraction of cooperators observed with degree-correlated activity therefore vanish, and so does the need for the lengthy spatiotemporal reorganization of compact cooperative clusters. The absence of such asymmetric dynamic instabilities thus leads to an optimal resolution of social dilemmas, especially when the conditions for the evolution of cooperation are strongly adverse.
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Affiliation(s)
- Alberto Aleta
- Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Zaragoza E-50018, Spain
| | - Sandro Meloni
- Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Zaragoza E-50018, Spain
- Department of Theoretical Physics, University of Zaragoza, Zaragoza E-50009, Spain
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, Maribor SI-2000, Slovenia
- CAMTP - Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, Maribor SI-2000, Slovenia
| | - Yamir Moreno
- Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, Zaragoza E-50018, Spain
- Department of Theoretical Physics, University of Zaragoza, Zaragoza E-50009, Spain
- Complex Networks and Systems Lagrange Lab, Institute for Scientific Interchange, Turin 10126, Italy
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13
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Burgos AC, Polani D. Cooperation and antagonism in information exchange in a growth scenario with two species. J Theor Biol 2016; 399:117-33. [DOI: 10.1016/j.jtbi.2016.04.006] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2015] [Revised: 02/28/2016] [Accepted: 04/01/2016] [Indexed: 11/15/2022]
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14
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Szolnoki A, Perc M. Leaders should not be conformists in evolutionary social dilemmas. Sci Rep 2016; 6:23633. [PMID: 27004605 PMCID: PMC4804302 DOI: 10.1038/srep23633] [Citation(s) in RCA: 85] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2016] [Accepted: 03/10/2016] [Indexed: 11/17/2022] Open
Abstract
The most common assumption in evolutionary game theory is that players should adopt a strategy that warrants the highest payoff. However, recent studies indicate that the spatial selection for cooperation is enhanced if an appropriate fraction of the population chooses the most common rather than the most profitable strategy within the interaction range. Such conformity might be due to herding instincts or crowd behavior in humans and social animals. In a heterogeneous population where individuals differ in their degree, collective influence, or other traits, an unanswered question remains who should conform. Selecting conformists randomly is the simplest choice, but it is neither a realistic nor the optimal one. We show that, regardless of the source of heterogeneity and game parametrization, socially the most favorable outcomes emerge if the masses conform. On the other hand, forcing leaders to conform significantly hinders the constructive interplay between heterogeneity and coordination, leading to evolutionary outcomes that are worse still than if conformists were chosen randomly. We conclude that leaders must be able to create a following for network reciprocity to be optimally augmented by conformity. In the opposite case, when leaders are castrated and made to follow, the failure of coordination impairs the evolution of cooperation.
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Affiliation(s)
- Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
- CAMTP – Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia
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15
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Collective punishment is more effective than collective reward for promoting cooperation. Sci Rep 2015; 5:17752. [PMID: 26634907 PMCID: PMC4669458 DOI: 10.1038/srep17752] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Accepted: 10/16/2015] [Indexed: 11/17/2022] Open
Abstract
Collective punishment and reward are usually regarded as two potential mechanisms to explain the evolution of cooperation. Both scenarios, however, seem problematic to understand cooperative behavior, because they can raise the second-order free-rider problem and many organisms are not able to discriminate less cooperating individuals. Even though they have been proved to increase cooperation, there has been a debate about which one being more effective. To address this issue, we resort to the N-player evolutionary snowdrift game (NESG), where a collective punishment/reward mechanism is added by allowing some players to display punishment/reward towards all remaining players. By means of numerous simulations and analyses, we find that collective punishment is more effective in promoting cooperation for a relatively high initial frequency of cooperation or for a relatively small group. When the intensity of punishment exceeds a certain threshold, a stable state of full cooperation emerges for both small and large groups. In contrast, such state does not appear for large groups playing a NESG with reward mechanism. In the case of mutualistic interactions, finally, our results show the new payoff with collective punishment/reward can lead to the coexistence of cooperators and defectors when discrimination between these two is not possible.
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16
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Wang Z, Andrews MA, Wu ZX, Wang L, Bauch CT. Coupled disease-behavior dynamics on complex networks: A review. Phys Life Rev 2015; 15:1-29. [PMID: 26211717 PMCID: PMC7105224 DOI: 10.1016/j.plrev.2015.07.006] [Citation(s) in RCA: 163] [Impact Index Per Article: 18.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2015] [Revised: 06/24/2015] [Accepted: 06/25/2015] [Indexed: 01/30/2023]
Abstract
It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease-behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease-behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years.
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Affiliation(s)
- Zhen Wang
- School of Automation, Northwestern Polytechnical University, Xi'an 710072, China; Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka, 816-8580, Japan.
| | - Michael A Andrews
- Department of Mathematics and Statistics, University of Guelph, Guelph, ON, N1G 2W1, Canada.
| | - Zhi-Xi Wu
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000, China.
| | - Lin Wang
- School of Computer and Communication Engineering, Tianjin University of Technology, Tianjin 300384, China.
| | - Chris T Bauch
- Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
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17
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Universal scaling for the dilemma strength in evolutionary games. Phys Life Rev 2015; 14:1-30. [PMID: 25979121 DOI: 10.1016/j.plrev.2015.04.033] [Citation(s) in RCA: 136] [Impact Index Per Article: 15.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Revised: 04/20/2015] [Accepted: 04/20/2015] [Indexed: 11/24/2022]
Abstract
Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.
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Zhang L, Zou Y, Guan S, Liu Z. Analytical description for the critical fixations of evolutionary coordination games on finite complex structured populations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042807. [PMID: 25974547 DOI: 10.1103/physreve.91.042807] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2014] [Indexed: 06/04/2023]
Abstract
Evolutionary game theory is crucial to capturing the characteristic interaction patterns among selfish individuals. In a population of coordination games of two strategies, one of the central problems is to determine the fixation probability that the system reaches a state of networkwide of only one strategy, and the corresponding expectation times. The deterministic replicator equations predict the critical value of initial density of one strategy, which separates the two absorbing states of the system. However, numerical estimations of this separatrix show large deviations from the theory in finite populations. Here we provide a stochastic treatment of this dynamic process on complex networks of finite sizes as Markov processes, showing the evolutionary time explicitly. We describe analytically the effects of network structures on the intermediate fixations as observed in numerical simulations. Our theoretical predictions are validated by various simulations on both random and scale free networks. Therefore, our stochastic framework can be helpful in dealing with other networked game dynamics.
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Affiliation(s)
- Liye Zhang
- Department of Physics, East China Normal University, Shanghai 200062, China
| | - Yong Zou
- Department of Physics, East China Normal University, Shanghai 200062, China
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Shuguang Guan
- Department of Physics, East China Normal University, Shanghai 200062, China
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zonghua Liu
- Department of Physics, East China Normal University, Shanghai 200062, China
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
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Szolnoki A, Perc M. Conformity enhances network reciprocity in evolutionary social dilemmas. J R Soc Interface 2015; 12:20141299. [PMID: 25540242 PMCID: PMC4305429 DOI: 10.1098/rsif.2014.1299] [Citation(s) in RCA: 160] [Impact Index Per Article: 17.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2014] [Accepted: 12/04/2014] [Indexed: 11/12/2022] Open
Abstract
The pursuit of highest payoffs in evolutionary social dilemmas is risky and sometimes inferior to conformity. Choosing the most common strategy within the interaction range is safer because it ensures that the payoff of an individual will not be much lower than average. Herding instincts and crowd behaviour in humans and social animals also compel to conformity in their own right. Motivated by these facts, we here study the impact of conformity on the evolution of cooperation in social dilemmas. We show that an appropriate fraction of conformists within the population introduces an effective surface tension around cooperative clusters and ensures smooth interfaces between different strategy domains. Payoff-driven players brake the symmetry in favour of cooperation and enable an expansion of clusters past the boundaries imposed by traditional network reciprocity. This mechanism works even under the most testing conditions, and it is robust against variations of the interaction network as long as degree-normalized payoffs are applied. Conformity may thus be beneficial for the resolution of social dilemmas.
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Affiliation(s)
- Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, PO Box 49, 1525 Budapest, Hungary
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia Department of Physics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, 2000 Maribor, Slovenia
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20
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Wu ZX, Rong Z. Boosting cooperation by involving extortion in spatial prisoner's dilemma games. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062102. [PMID: 25615039 DOI: 10.1103/physreve.90.062102] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2014] [Indexed: 05/25/2023]
Abstract
We study the evolution of cooperation in spatial prisoner's dilemma games with and without extortion by adopting the aspiration-driven strategy updating rule. We focus explicitly on how the strategy updating manner (whether synchronous or asynchronous) and also the introduction of extortion strategy affect the collective outcome of the games. By means of Monte Carlo simulations as well as dynamical cluster techniques, we find that the involvement of extortioners facilitates the boom of cooperators in the population (and whom can always dominate the population if the temptation to defect is not too large) for both synchronous and asynchronous strategy updating, in stark contrast to the other case, where cooperation is promoted for an intermediate aspiration level with synchronous strategy updating, but is remarkably inhibited if the strategy updating is implemented asynchronously. We explain the results by configurational analysis and find that the presence of extortion leads to the checkerboard-like ordering of cooperators and extortioners, which enable cooperators to prevail in the population with both strategy updating manners. Moreover, extortion itself is evolutionary stable, and therefore acts as the incubator for the evolution of cooperation.
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Affiliation(s)
- Zhi-Xi Wu
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou Gansu 730000, China
| | - Zhihai Rong
- CompleX Lab, Web Sciences Center, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China and Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong
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21
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Wang X, Wu J, Shu G, Li Y. Punishment based on public benefit fund significantly promotes cooperation. PLoS One 2014; 9:e105126. [PMID: 25137051 PMCID: PMC4138163 DOI: 10.1371/journal.pone.0105126] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2014] [Accepted: 07/18/2014] [Indexed: 11/19/2022] Open
Abstract
In prisoner's dilemma game (shortly, PD game), punishment is most frequently used to promote cooperation. However, outcome varies when different punishment approaches are applied. Here the PD game is studied on a square lattice when different punishment patterns are adopted. As is known to all, tax system, a common tool to adjust the temperature of the economy, is widely used in human society. Inspired by this philosophy, players in this study would pay corresponding taxes in accordance with their payoff level. In this way, public benefit fund is established consequently and it would be utilized to punish defectors. There are two main methods for punishing: slight intensity of punishment (shortly, SLP) and severe intensity of punishment (shortly, SEP). When the totaling of public benefit fund keeps relatively fixed, SLP extends further, which means more defectors would be punished; by contrast, SEP has a smaller coverage. It is of interest to verify whether these two measures can promote cooperation and which one is more efficient. Simulate results reveal that both of them can promote cooperation remarkably. Specifically speaking, SLP shows constant advantage from the point of view either of fractions of cooperation or average payoff.
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Affiliation(s)
- Xiuling Wang
- School of Computer and Information Science, Southwest University, Chongqing, China
| | - Jie Wu
- School of Computer and Information Science, Southwest University, Chongqing, China
| | - Gang Shu
- School of Physical Science and Technology, Southwest University, Chongqing, China
| | - Ya Li
- School of Computer and Information Science, Southwest University, Chongqing, China
- * E-mail:
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22
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Li Y. The evolution of reputation-based partner-switching behaviors with a cost. Sci Rep 2014; 4:5957. [PMID: 25091006 PMCID: PMC4121600 DOI: 10.1038/srep05957] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2014] [Accepted: 07/16/2014] [Indexed: 11/09/2022] Open
Abstract
Humans constantly adjust their social relationships and choose new partners of good reputations, thereby promoting the evolution of cooperation. Individuals have to pay a cost to build a reputation, obtain others' information and then make partnership adjustments, yet the conditions under which such costly behaviors are able to evolve remain to be explored. In this model, I assume that individuals have to pay a cost to adjust their partnerships. Furthermore, whether an individual can adjust his partnership based on reputation is determined by his strategic preference, which is updated via coevolution. Using the metaphor of a public goods game where the collective benefit is shared among all members of a group, the coupling dynamics of cooperation and partnership adjustment were numerically simulated. Partner-switching behavior cannot evolve in a public goods game with a low amplification factor. However, such an effect can be exempted by raising the productivity of public goods or the frequency of partnership adjustment. Moreover, costly partner-switching behavior is remarkably promoted by the condition that the mechanism of reputation evaluation considers its prosociality. A mechanism of reputation evaluation that praises both cooperative and partner-switching behaviors allows them to coevolve.
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Affiliation(s)
- Yixiao Li
- School of Information, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang 310018, China
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23
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Wang Z, Wang L, Perc M. Degree mixing in multilayer networks impedes the evolution of cooperation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052813. [PMID: 25353850 DOI: 10.1103/physreve.89.052813] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2013] [Indexed: 05/05/2023]
Abstract
Traditionally, the evolution of cooperation has been studied on single, isolated networks. Yet a player, especially in human societies, will typically be a member of many different networks, and those networks will play different roles in the evolutionary process. Multilayer networks are therefore rapidly gaining on popularity as the more apt description of a networked society. With this motivation, we here consider two-layer scale-free networks with all possible combinations of degree mixing, wherein one network layer is used for the accumulation of payoffs and the other is used for strategy updating. We find that breaking the symmetry through assortative mixing in one layer and/or disassortative mixing in the other layer, as well as preserving the symmetry by means of assortative mixing in both layers, impedes the evolution of cooperation. We use degree-dependent distributions of strategies and cluster-size analysis to explain these results, which highlight the importance of hubs and the preservation of symmetry between multilayer networks for the successful resolution of social dilemmas.
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Affiliation(s)
- Zhen Wang
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong and Center for Nonlinear Studies and Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems, Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | - Lin Wang
- Centre for Chaos and Complex Networks, Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
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24
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Szolnoki A, Perc M. Evolution of extortion in structured populations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:022804. [PMID: 25353531 DOI: 10.1103/physreve.89.022804] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2013] [Indexed: 05/08/2023]
Abstract
Extortion strategies can dominate any opponent in an iterated prisoner's dilemma game. But if players are able to adopt the strategies performing better, extortion becomes widespread and evolutionary unstable. It may sometimes act as a catalyst for the evolution of cooperation, and it can also emerge in interactions between two populations, yet it is not the evolutionarily stable outcome. Here we revisit these results in the realm of spatial games. We find that pairwise imitation and birth-death dynamics return known evolutionary outcomes. Myopic best response strategy updating, on the other hand, reveals counterintuitive solutions. Defectors and extortioners coarsen spontaneously, which allows cooperators to prevail even at prohibitively high temptations to defect. Here extortion strategies play the role of a Trojan horse. They may emerge among defectors by chance, and once they do, cooperators become viable as well. These results are independent of the interaction topology, and they highlight the importance of coarsening, checkerboard ordering, and best response updating in evolutionary games.
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Affiliation(s)
- Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
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25
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Wu ZX, Yang HX. Social dilemma alleviated by sharing the gains with immediate neighbors. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012109. [PMID: 24580174 DOI: 10.1103/physreve.89.012109] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2013] [Indexed: 06/03/2023]
Abstract
We study the evolution of cooperation in the evolutionary spatial prisoner's dilemma game (PDG) and snowdrift game (SG), within which a fraction α of the payoffs of each player gained from direct game interactions is shared equally by the immediate neighbors. The magnitude of the parameter α therefore characterizes the degree of the relatedness among the neighboring players. By means of extensive Monte Carlo simulations as well as an extended mean-field approximation method, we trace the frequency of cooperation in the stationary state. We find that plugging into relatedness can significantly promote the evolution of cooperation in the context of both studied games. Unexpectedly, cooperation can be more readily established in the spatial PDG than that in the spatial SG, given that the degree of relatedness and the cost-to-benefit ratio of mutual cooperation are properly formulated. The relevance of our model with the stakeholder theory is also briefly discussed.
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Affiliation(s)
- Zhi-Xi Wu
- Institute of Computational Physics and Complex Systems, Lanzhou University, Lanzhou Gansu 730000, China
| | - Han-Xin Yang
- Department of Physics, Fuzhou University, Fuzhou 350108, China
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26
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Nepusz T, Vicsek T. Hierarchical self-organization of non-cooperating individuals. PLoS One 2013; 8:e81449. [PMID: 24349070 PMCID: PMC3859486 DOI: 10.1371/journal.pone.0081449] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2013] [Accepted: 10/11/2013] [Indexed: 11/18/2022] Open
Abstract
Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the units they are made of according to a network displaying hierarchical features. In spite of the abundant presence of hierarchy no quantitative theoretical interpretation of the origins of a multi-level, knowledge-based social network exists. Here we introduce an approach which is capable of reproducing the emergence of a multi-levelled network structure based on the plausible assumption that the individuals (representing the nodes of the network) can make the right estimate about the state of their changing environment to a varying degree. Our model accounts for a fundamental feature of knowledge-based organizations: the less capable individuals tend to follow those who are better at solving the problems they all face. We find that relatively simple rules lead to hierarchical self-organization and the specific structures we obtain possess the two, perhaps most important features of complex systems: a simultaneous presence of adaptability and stability. In addition, the performance (success score) of the emerging networks is significantly higher than the average expected score of the individuals without letting them copy the decisions of the others. The results of our calculations are in agreement with a related experiment and can be useful from the point of designing the optimal conditions for constructing a given complex social structure as well as understanding the hierarchical organization of such biological structures of major importance as the regulatory pathways or the dynamics of neural networks.
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Affiliation(s)
- Tamás Nepusz
- Department of Biological Physics, Eötvös University, Budapest, Hungary
| | - Tamás Vicsek
- Department of Biological Physics, Eötvös University, Budapest, Hungary
- Statistical and Biological Physics Research Group of the Hungarian Academy of Sciences, Budapest, Hungary
- * E-mail:
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27
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Krause SM, Peixoto TP, Bornholdt S. Spontaneous centralization of control in a network of company ownerships. PLoS One 2013; 8:e80303. [PMID: 24324594 PMCID: PMC3855616 DOI: 10.1371/journal.pone.0080303] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2013] [Accepted: 10/11/2013] [Indexed: 11/18/2022] Open
Abstract
We introduce a model for the adaptive evolution of a network of company ownerships. In a recent work it has been shown that the empirical global network of corporate control is marked by a central, tightly connected “core” made of a small number of large companies which control a significant part of the global economy. Here we show how a simple, adaptive “rich get richer” dynamics can account for this characteristic, which incorporates the increased buying power of more influential companies, and in turn results in even higher control. We conclude that this kind of centralized structure can emerge without it being an explicit goal of these companies, or as a result of a well-organized strategy.
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Affiliation(s)
- Sebastian M. Krause
- Institut für Theoretische Physik, Universität Bremen, Bremen, Germany
- * E-mail:
| | - Tiago P. Peixoto
- Institut für Theoretische Physik, Universität Bremen, Bremen, Germany
| | - Stefan Bornholdt
- Institut für Theoretische Physik, Universität Bremen, Bremen, Germany
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28
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Szolnoki A, Perc M. Decelerated invasion and waning-moon patterns in public goods games with delayed distribution. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:054801. [PMID: 23767662 DOI: 10.1103/physreve.87.054801] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2013] [Indexed: 06/02/2023]
Abstract
We study the evolution of cooperation in the spatial public goods game, focusing on the effects that are brought about by the delayed distribution of goods that accumulate in groups due to the continuous investments of cooperators. We find that intermediate delays enhance network reciprocity because of a decelerated invasion of defectors, who are unable to reap the same high short-term benefits as they do in the absence of delayed distribution. Long delays, however, introduce a risk because the large accumulated wealth might fall into the wrong hands. Indeed, as soon as the curvature of a cooperative cluster turns negative, the engulfed defectors can collect the heritage of many generations of cooperators and by doing so start a waning-moon pattern that nullifies the benefits of decelerated invasion. Accidental meeting points of growing cooperative clusters may also act as triggers for the waning-moon effect, thus linking the success of cooperators with their propensity to fail in a rather bizarre way. Our results highlight that "investing in the future" is a good idea only if that future is sufficiently near and not likely to be burdened by inflation.
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Affiliation(s)
- Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
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29
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Szolnoki A, Xie NG, Ye Y, Perc M. Evolution of emotions on networks leads to the evolution of cooperation in social dilemmas. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:042805. [PMID: 23679471 DOI: 10.1103/physreve.87.042805] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2012] [Indexed: 06/02/2023]
Abstract
We show that the resolution of social dilemmas in random graphs and scale-free networks is facilitated by imitating not the strategy of better-performing players but, rather, their emotions. We assume sympathy and envy to be the two emotions that determine the strategy of each player in any given interaction, and we define them as the probabilities of cooperating with players having a lower and a higher payoff, respectively. Starting with a population where all possible combinations of the two emotions are available, the evolutionary process leads to a spontaneous fixation to a single emotional profile that is eventually adopted by all players. However, this emotional profile depends not only on the payoffs but also on the heterogeneity of the interaction network. Homogeneous networks, such as lattices and regular random graphs, lead to fixations that are characterized by high sympathy and high envy, while heterogeneous networks lead to low or modest sympathy but also low envy. Our results thus suggest that public emotions and the propensity to cooperate at large depend, and are in fact determined by, the properties of the interaction network.
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Affiliation(s)
- Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary.
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30
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Wang X. Forming mechanisms and structures of a knowledge transfer network: theoretical and simulation research. JOURNAL OF KNOWLEDGE MANAGEMENT 2013. [DOI: 10.1108/13673271311315213] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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31
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Wang Z, Szolnoki A, Perc M. Interdependent network reciprocity in evolutionary games. Sci Rep 2013; 3:1183. [PMID: 23378915 PMCID: PMC3560361 DOI: 10.1038/srep01183] [Citation(s) in RCA: 333] [Impact Index Per Article: 30.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2012] [Accepted: 01/15/2013] [Indexed: 12/04/2022] Open
Abstract
Besides the structure of interactions within networks, also the interactions between networks are of the outmost importance. We therefore study the outcome of the public goods game on two interdependent networks that are connected by means of a utility function, which determines how payoffs on both networks jointly influence the success of players in each individual network. We show that an unbiased coupling allows the spontaneous emergence of interdependent network reciprocity, which is capable to maintain healthy levels of public cooperation even in extremely adverse conditions. The mechanism, however, requires simultaneous formation of correlated cooperator clusters on both networks. If this does not emerge or if the coordination process is disturbed, network reciprocity fails, resulting in the total collapse of cooperation. Network interdependence can thus be exploited effectively to promote cooperation past the limits imposed by isolated networks, but only if the coordination between the interdependent networks is not disturbed.
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Affiliation(s)
- Zhen Wang
- Department of Physics Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Center for Nonlinear Studies and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems, Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | - Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of SciencesP.O. Box 49, H-1525 Budapest, Hungary
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
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32
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Wang Z, Szolnoki A, Perc M. Optimal interdependence between networks for the evolution of cooperation. Sci Rep 2013; 3:2470. [PMID: 23959086 PMCID: PMC3747507 DOI: 10.1038/srep02470] [Citation(s) in RCA: 74] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2013] [Accepted: 08/02/2013] [Indexed: 11/17/2022] Open
Abstract
Recent research has identified interactions between networks as crucial for the outcome of evolutionary games taking place on them. While the consensus is that interdependence does promote cooperation by means of organizational complexity and enhanced reciprocity that is out of reach on isolated networks, we here address the question just how much interdependence there should be. Intuitively, one might assume the more the better. However, we show that in fact only an intermediate density of sufficiently strong interactions between networks warrants an optimal resolution of social dilemmas. This is due to an intricate interplay between the heterogeneity that causes an asymmetric strategy flow because of the additional links between the networks, and the independent formation of cooperative patterns on each individual network. Presented results are robust to variations of the strategy updating rule, the topology of interdependent networks, and the governing social dilemma, thus suggesting a high degree of universality.
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Affiliation(s)
- Zhen Wang
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Center for Nonlinear Studies and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems, Hong Kong Baptist University, Kowloon Tong, Hong Kong
| | - Attila Szolnoki
- Institute of Technical Physics and Materials Science, Research Centre for Natural Sciences, Hungarian Academy of SciencesP.O. Box 49, H-1525 Budapest, Hungary
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
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33
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Beyond pairwise strategy updating in the prisoner's dilemma game. Sci Rep 2012; 2:740. [PMID: 23074647 PMCID: PMC3472391 DOI: 10.1038/srep00740] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/22/2012] [Accepted: 09/25/2012] [Indexed: 11/09/2022] Open
Abstract
In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.
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34
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Peixoto TP, Bornholdt S. No need for conspiracy: self-organized cartel formation in a modified trust game. PHYSICAL REVIEW LETTERS 2012; 108:218702. [PMID: 23003311 DOI: 10.1103/physrevlett.108.218702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2012] [Indexed: 06/01/2023]
Abstract
We investigate the dynamics of a trust game on a mixed population, where individuals with the role of buyers are forced to play against a predetermined number of sellers whom they choose dynamically. Agents with the role of sellers are also allowed to adapt the level of value for money of their products, based on payoff. The dynamics undergoes a transition at a specific value of the strategy update rate, above which an emergent cartel organization is observed, where sellers have similar values of below-optimal value for money. This cartel organization is not due to an explicit collusion among agents; instead, it arises spontaneously from the maximization of the individual payoffs. This dynamics is marked by large fluctuations and a high degree of unpredictability for most of the parameter space and serves as a plausible qualitative explanation for observed elevated levels and fluctuations of certain commodity prices.
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Affiliation(s)
- Tiago P Peixoto
- Institut für Theoretische Physik, Universität Bremen, Bremen, Germany.
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35
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Adaptive and bounded investment returns promote cooperation in spatial public goods games. PLoS One 2012; 7:e36895. [PMID: 22615836 PMCID: PMC3353963 DOI: 10.1371/journal.pone.0036895] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2012] [Accepted: 04/09/2012] [Indexed: 11/26/2022] Open
Abstract
The public goods game is one of the most famous models for studying the evolution of cooperation in sizable groups. The multiplication factor in this game can characterize the investment return from the public good, which may be variable depending on the interactive environment in realistic situations. Instead of using the same universal value, here we consider that the multiplication factor in each group is updated based on the differences between the local and global interactive environments in the spatial public goods game, but meanwhile limited to within a certain range. We find that the adaptive and bounded investment returns can significantly promote cooperation. In particular, full cooperation can be achieved for high feedback strength when appropriate limitation is set for the investment return. Also, we show that the fraction of cooperators in the whole population can become larger if the lower and upper limits of the multiplication factor are increased. Furthermore, in comparison to the traditionally spatial public goods game where the multiplication factor in each group is identical and fixed, we find that cooperation can be better promoted if the multiplication factor is constrained to adjust between one and the group size in our model. Our results highlight the importance of the locally adaptive and bounded investment returns for the emergence and dominance of cooperative behavior in structured populations.
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36
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Wang Z, Szolnoki A, Perc M. If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation. Sci Rep 2012; 2:369. [PMID: 22511999 PMCID: PMC3328045 DOI: 10.1038/srep00369] [Citation(s) in RCA: 161] [Impact Index Per Article: 13.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2012] [Accepted: 03/29/2012] [Indexed: 12/04/2022] Open
Abstract
Spatial reciprocity is a well known tour de force of cooperation promotion. A thorough understanding of the effects of different population densities is therefore crucial. Here we study the evolution of cooperation in social dilemmas on different interaction graphs with a certain fraction of vacant nodes. We find that sparsity may favor the resolution of social dilemmas, especially if the population density is close to the percolation threshold of the underlying graph. Regardless of the type of the governing social dilemma as well as particularities of the interaction graph, we show that under pairwise imitation the percolation threshold is a universal indicator of how dense the occupancy ought to be for cooperation to be optimally promoted. We also demonstrate that myopic updating, due to the lack of efficient spread of information via imitation, renders the reported mechanism dysfunctional, which in turn further strengthens its foundations.
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37
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Wang Z, Szolnoki A, Perc M. Percolation threshold determines the optimal population density for public cooperation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:037101. [PMID: 22587213 DOI: 10.1103/physreve.85.037101] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/27/2011] [Indexed: 05/31/2023]
Abstract
While worldwide census data provide statistical evidence that firmly link the population density with several indicators of social welfare, the precise mechanisms underlying these observations are largely unknown. Here we study the impact of population density on the evolution of public cooperation in structured populations and find that the optimal density is uniquely related to the percolation threshold of the host graph irrespective of its topological details. We explain our observations by showing that spatial reciprocity peaks in the vicinity of the percolation threshold, when the emergence of a giant cooperative cluster is hindered neither by vacancy nor by invading defectors, thus discovering an intuitive yet universal law that links the population density with social prosperity.
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Affiliation(s)
- Zhen Wang
- School of Physics, Nankai University, Tianjin 300071, China
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38
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Win-stay-lose-learn promotes cooperation in the spatial prisoner's dilemma game. PLoS One 2012; 7:e30689. [PMID: 22363470 PMCID: PMC3281853 DOI: 10.1371/journal.pone.0030689] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2011] [Accepted: 12/21/2011] [Indexed: 11/19/2022] Open
Abstract
Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed win-stay-lose-learn rule promotes the evolution of cooperation, and it does so very robustly and independently of the initial conditions. In fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related win-stay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma.
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39
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Li PP, Ke J, Lin Z, Hui PM. Cooperative behavior in evolutionary snowdrift games with the unconditional imitation rule on regular lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021111. [PMID: 22463157 DOI: 10.1103/physreve.85.021111] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2011] [Revised: 11/30/2011] [Indexed: 05/31/2023]
Abstract
We study an evolutionary snowdrift game with the unconditional imitation updating rule on regular lattices. Detailed numerical simulations establish the structure of plateaus and discontinuous jumps of the equilibrium cooperation frequency f(c) as a function of the cost-to-benefit ratio r. By analyzing the stability of local configurations, it is found that the transitions occur at values of r at which there are changes in the ranking of the payoffs to the different local configurations of agents using different strategies. Nonmonotonic behavior of f(c)(r) at the intermediate range of r is analyzed in terms of the formation of blocks of agents using the cooperative strategy that are stabilized by agents inside the block due to the updating rule. For random initial condition with 50%-50% agents of different strategies randomly dispersed, cooperation persists in the whole range of r and the level of cooperation is higher than that in the well-mixed case in a wide range of r. These results are in sharp contrast to those based on the replicator updating rule. The sensitivity to initial states with different fractions of cooperative agents is also discussed. The results serve to illustrate that both the spatial structure and the updating rule are important in determining the level of cooperation in a competing population. When extreme initial states are used where there are very few agents of a strategy in a background of the opposite strategy, the result would depend on the stability of the clusters formed by the initially minority agents.
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Affiliation(s)
- Ping-Ping Li
- College of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou 325035, China
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40
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Szolnoki A, Perc M. Conditional strategies and the evolution of cooperation in spatial public goods games. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:026104. [PMID: 22463276 DOI: 10.1103/physreve.85.026104] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2011] [Revised: 01/12/2012] [Indexed: 05/31/2023]
Abstract
The fact that individuals will most likely behave differently in different situations begets the introduction of conditional strategies. Inspired by this, we study the evolution of cooperation in the spatial public goods game, where, besides unconditional cooperators and defectors, also different types of conditional cooperators compete for space. Conditional cooperators will contribute to the public good only if other players within the group are likely to cooperate as well but will withhold their contribution otherwise. Depending on the number of other cooperators that are required to elicit cooperation of a conditional cooperator, the latter can be classified in as many types as there are players within each group. We find that the most cautious cooperators, who require all other players within a group to be conditional cooperators, are the undisputed victors of the evolutionary process, even at very low synergy factors. We show that the remarkable promotion of cooperation is due primarily to the spontaneous emergence of quarantining of defectors, who become surrounded by conditional cooperators and are forced into isolated convex "bubbles" from which they are unable to exploit the public good. This phenomenon can be observed only in structured populations, thus adding to the relevance of pattern formation for the successful evolution of cooperation.
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Affiliation(s)
- Attila Szolnoki
- Research Institute for Technical Physics and Materials Science, PO Box 49, H-1525 Budapest, Hungary
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41
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Requejo RJ, Camacho J. Coexistence of cooperators and defectors in well mixed populations mediated by limiting resources. PHYSICAL REVIEW LETTERS 2012; 108:038701. [PMID: 22400794 DOI: 10.1103/physrevlett.108.038701] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2011] [Indexed: 05/31/2023]
Abstract
Traditionally, resource limitation in evolutionary game theory is assumed just to impose a constant population size. Here we show that resource limitations may generate dynamical payoffs able to alter an original prisoner's dilemma, and to allow for the stable coexistence between unconditional cooperators and defectors in well-mixed populations. This is a consequence of a self-organizing process that turns the interaction payoff matrix into evolutionary neutral, and represents a resource-based control mechanism preventing the spread of defectors. To our knowledge, this is the first example of coexistence in well-mixed populations with a game structure different from a snowdrift game.
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Affiliation(s)
- R J Requejo
- Departament de Física, Universitat Autònoma de Barcelona, Campus UAB, E-08193 Bellaterra, Spain
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42
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Lee S, Holme P, Wu ZX. Cooperation, structure, and hierarchy in multiadaptive games. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:061148. [PMID: 22304081 DOI: 10.1103/physreve.84.061148] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2011] [Revised: 12/05/2011] [Indexed: 05/31/2023]
Abstract
Game-theoretical models where the rules of the game and the interaction structure both coevolve with the game dynamics--multiadaptive games--capture very flexible situations where cooperation among selfish agents can emerge. In this work, we will discuss a multiadaptive model presented in a recent Letter [Phys. Rev. Lett. 106, 028702 (2011)] as well as generalizations of it. The model captures a nonequilibrium situation where social unrest increases the incentive to cooperate and, simultaneously, agents are partly free to influence with whom they interact. First, we investigate the details of how feedback from the behavior of agents determines the emergence of cooperation and hierarchical contact structures. We also study the stability of the system to different types of noise, and find that different regions of parameter space show very different response. Some types of noise can destroy an all-cooperator (C) state. If, on the other hand, hubs are stable, then so is the all-C state. Finally, we investigate the dependence of the ratio between the time scales of strategy updates and the evolution of the interaction structure. We find that a comparatively fast strategy dynamics is a prerequisite for the emergence of cooperation.
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Affiliation(s)
- Sungmin Lee
- IceLab, Department of Physics, Umeå University, 90187 Umeå, Sweden
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Evolution of interactions and cooperation in the spatial prisoner's dilemma game. PLoS One 2011; 6:e26724. [PMID: 22066006 PMCID: PMC3204981 DOI: 10.1371/journal.pone.0026724] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2011] [Accepted: 10/02/2011] [Indexed: 11/19/2022] Open
Abstract
We study the evolution of cooperation in the spatial prisoner's dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation irrespective of game parametrization, the optimal number of new interactions depends somewhat on the temptation to defect. Our findings reveal that the "making of new friends" may be an important activity for the successful evolution of cooperation, but also that partners must be selected carefully and their number limited.
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44
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Perc M. Success-driven distribution of public goods promotes cooperation but preserves defection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:037102. [PMID: 22060534 DOI: 10.1103/physreve.84.037102] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2011] [Revised: 06/14/2011] [Indexed: 05/31/2023]
Abstract
Established already in Biblical times, the Matthew effect refers to the fact that in societies the rich tend to get richer and the potent even more powerful. Here we investigate a game theoretical model describing the evolution of cooperation on structured populations where the distribution of public goods is driven by the reproductive success of individuals. Phase diagrams reveal that cooperation is promoted irrespective of the uncertainty by strategy adoptions and the type of interaction graph, yet the complete dominance of cooperators is elusive due to the spontaneous emergence of superpersistent defectors that owe their survival to extremely rare microscopic patterns. This indicates that success-driven mechanisms are crucial for effectively harvesting benefits from collective actions but that they may also account for the observed persistence of maladaptive behavior.
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Affiliation(s)
- Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor, Slovenia
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