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Pattni K, Ali W, Broom M, Sharkey KJ. Eco-evolutionary dynamics in finite network-structured populations with migration. J Theor Biol 2023; 572:111587. [PMID: 37517517 DOI: 10.1016/j.jtbi.2023.111587] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2023] [Revised: 07/06/2023] [Accepted: 07/20/2023] [Indexed: 08/01/2023]
Abstract
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes. This allows complex interaction and migration behaviours that are dependent on competition. For migration, we assume that the response of individuals to competition is governed by tolerance to their group members, such that less tolerant individuals are more likely to move away due to competition. We look at the success of a mutant in the rare mutation limit for the complete, cycle and star networks. Unlike models with fixed population size and distribution, the distribution of the individuals per site is explicitly modelled by considering the dynamics of the population. This in turn determines the mutant appearance distribution for each network. Where a mutant appears impacts its success as it determines the competition it faces. For low and high migration rates the complete and cycle networks have similar mutant appearance distributions resulting in similar success levels for an invading mutant. A higher migration rate in the star network is detrimental for mutant success because migration results in a crowded central site where a mutant is more likely to appear.
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Affiliation(s)
- Karan Pattni
- Department of Mathematical Sciences, University of Liverpool, United Kingdom.
| | - Wajid Ali
- Department of Mathematical Sciences, University of Liverpool, United Kingdom
| | - Mark Broom
- Department of Mathematics, City, University of London, United Kingdom
| | - Kieran J Sharkey
- Department of Mathematical Sciences, University of Liverpool, United Kingdom
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2
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Ichinose G, Miyagawa D, Chiba E, Sayama H. How Lévy Flights Triggered by the Presence of Defectors Affect Evolution of Cooperation in Spatial Games. ARTIFICIAL LIFE 2023; 29:187-197. [PMID: 36018771 DOI: 10.1162/artl_a_00382] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Cooperation among individuals has been key to sustaining societies. However, natural selection favors defection over cooperation. Cooperation can be favored when the mobility of individuals allows cooperators to form a cluster (or group). Mobility patterns of animals sometimes follow a Lévy flight. A Lévy flight is a kind of random walk but it is composed of many small movements with a few big movements. The role of Lévy flights for cooperation has been studied by Antonioni and Tomassini, who showed that Lévy flights promoted cooperation combined with conditional movements triggered by neighboring defectors. However, the optimal condition for neighboring defectors and how the condition changes with the intensity of Lévy flights are still unclear. Here, we developed an agent-based model in a square lattice where agents perform Lévy flights depending on the fraction of neighboring defectors. We systematically studied the relationships among three factors for cooperation: sensitivity to defectors, the intensity of Lévy flights, and population density. Results of evolutionary simulations showed that moderate sensitivity most promoted cooperation. Then, we found that the shortest movements were best for cooperation when the sensitivity to defectors was high. In contrast, when the sensitivity was low, longer movements were best for cooperation. Thus, Lévy flights, the balance between short and long jumps, promoted cooperation in any sensitivity, which was confirmed by evolutionary simulations. Finally, as the population density became larger, higher sensitivity was more beneficial for cooperation to evolve. Our study highlights that Lévy flights are an optimal searching strategy not only for foraging but also for constructing cooperative relationships with others.
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Affiliation(s)
- Genki Ichinose
- Shizuoka University, Department of Mathematical and Systems Engineering.
| | - Daiki Miyagawa
- Shizuoka University, Department of Mathematical and Systems Engineering.
| | - Erika Chiba
- Nagoya University, Graduate School of Informatics.
| | - Hiroki Sayama
- Waseda University, Waseda Innovation Lab
- Binghamton University - SUNY, Center for Collective Dynamics of Complex Systems.
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3
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Shi Z, Wei W, Feng X, Li X, Zheng Z. Dynamic aspiration based on Win-Stay-Lose-Learn rule in spatial prisoner's dilemma game. PLoS One 2021; 16:e0244814. [PMID: 33395443 PMCID: PMC7781394 DOI: 10.1371/journal.pone.0244814] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2020] [Accepted: 12/16/2020] [Indexed: 11/18/2022] Open
Abstract
Prisoner’s dilemma game is the most commonly used model of spatial evolutionary game which is considered as a paradigm to portray competition among selfish individuals. In recent years, Win-Stay-Lose-Learn, a strategy updating rule base on aspiration, has been proved to be an effective model to promote cooperation in spatial prisoner’s dilemma game, which leads aspiration to receive lots of attention. In this paper, according to Expected Value Theory and Achievement Motivation Theory, we propose a dynamic aspiration model based on Win-Stay-Lose-Learn rule in which individual’s aspiration is inspired by its payoff. It is found that dynamic aspiration has a significant impact on the evolution process, and different initial aspirations lead to different results, which are called Stable Coexistence under Low Aspiration, Dependent Coexistence under Moderate aspiration and Defection Explosion under High Aspiration respectively. Furthermore, a deep analysis is performed on the local structures which cause defectors’ re-expansion, the concept of END- and EXP-periods are used to justify the mechanism of network reciprocity in view of time-evolution, typical feature nodes for defectors’ re-expansion called Infectors, Infected nodes and High-risk cooperators respectively are found. Compared to fixed aspiration model, dynamic aspiration introduces a more satisfactory explanation on population evolution laws and can promote deeper comprehension for the principle of prisoner’s dilemma.
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Affiliation(s)
- Zhenyu Shi
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
| | - Wei Wei
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
- * E-mail:
| | - Xiangnan Feng
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
| | - Xing Li
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
| | - Zhiming Zheng
- School of Mathematical Sciences, Beihang University, Beijing, China
- Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China
- Peng Cheng Laboratory, Shenzhen, Guangdong, China
- Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China
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4
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Self-organized habitat segregation in an ambush-predator system: Nonlinear migration of prey between two patches with finite capacities. ECOL INFORM 2020. [DOI: 10.1016/j.ecoinf.2019.101022] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
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5
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The influence of heterogeneous learning ability on the evolution of cooperation. Sci Rep 2019; 9:13920. [PMID: 31558763 PMCID: PMC6763452 DOI: 10.1038/s41598-019-50451-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/06/2019] [Accepted: 09/04/2019] [Indexed: 11/08/2022] Open
Abstract
In this paper, we design a simple coevolution model to investigate the role of heterogeneous learning ability on the evolution of cooperation. The model weakens the winner's learning ability in order to keep its current advantage. Conversely, it strengthens the loser's learning ability for increasing the chance to update its strategy. In particular, we consider this coevolutionary model separately applying to both cooperators and defectors (rule I), only cooperators (rule II), as well as only defectors (rule III) in spatial prisoner's dilemma game. Through numerical simulations, we find that cooperation can be promoted in rule II, whereas, cooperation is hampered in rule I and rule III. We reveal its potential reason from the viewpoint of enduring and expanding periods in game dynamics. Our results thus provide a deeper understanding regarding the heterogeneous learning ability on game theory.
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6
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Yokoi H, Tainaka KI, Sato K. Metapopulation model for a prey-predator system: Nonlinear migration due to the finite capacities of patches. J Theor Biol 2019; 477:24-35. [PMID: 31194986 DOI: 10.1016/j.jtbi.2019.05.021] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2019] [Revised: 05/29/2019] [Accepted: 05/31/2019] [Indexed: 10/26/2022]
Abstract
Many species live in spatially separated patches, and individuals can migrate between patches through paths. In real ecosystems, the capacities of patches are finite. If a patch is already occupied by the individuals of some species, then the migration into the patch is impossible. In the present paper, we deal with prey-predator system composed of two patches. Each patch contains a limited number of cells, where the cell is either empty or occupied by an individual of prey or predator. We introduce "swapping migration" defined by the exchange between occupied and empty cells. An individual can migrate, only when there are empty cells in the destination patch. Reaction-migration equations in prey-predator system are presented, where the migration term forms nonlinear function of densities. We numerically solve equilibrium densities, and find that the population dynamics are largely affected by nonlinear migration. Not only extinction points but also the responses to the environmental changes crucially depend on the patch capacities.
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Affiliation(s)
- Hiroki Yokoi
- National Research Institute of Far Seas Fisheries, Fisheries Research Agency, 5-7-1, Orido, Shimizu, Shizuoka 424-8633, Japan
| | - Kei-Ichi Tainaka
- Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan
| | - Kazunori Sato
- Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.
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Shen C, Chu C, Shi L, Perc M, Wang Z. Aspiration-based coevolution of link weight promotes cooperation in the spatial prisoner's dilemma game. ROYAL SOCIETY OPEN SCIENCE 2018; 5:180199. [PMID: 29892454 PMCID: PMC5990773 DOI: 10.1098/rsos.180199] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2018] [Accepted: 03/23/2018] [Indexed: 05/24/2023]
Abstract
In this article, we propose an aspiration-based coevolution of link weight, and explore how this set-up affects the evolution of cooperation in the spatial prisoner's dilemma game. In particular, an individual will increase the weight of its link to its neighbours only if the payoff received via this interaction exceeds a pre-defined aspiration. Conversely, if the received payoff is below this aspiration, the link weight with the corresponding neighbour will decrease. Our results show that an appropriate aspiration level leads to a high-cooperation plateau, whereas too high or too low aspiration will impede the evolution of cooperation. We explain these findings with a comprehensive analysis of transition points and with a systematic analysis of typical configuration patterns. The presented results provide further theoretical insights with regards to the impact of different aspiration levels on cooperation in human societies.
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Affiliation(s)
- Chen Shen
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, People's Republic of China
| | - Chen Chu
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, People's Republic of China
| | - Lei Shi
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, People's Republic of China
| | - Matjaž Perc
- Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska cesta 160, 2000 Maribor, Slovenia
- CAMTP—Center for Applied Mathematics and Theoretical Physics, University of Maribor, Mladinska 3, 2000 Maribor, Slovenia
- Complexity Science Hub, Josefstädterstraße 39, 1080 Vienna, Austria
| | - Zhen Wang
- School of Mechanical Engineering and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an 710072, People's Republic of China
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8
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Herrera M, Miller A, Nishimura J. Altruistic aging: The evolutionary dynamics balancing longevity and evolvability. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2017; 14:455-465. [PMID: 27879109 DOI: 10.3934/mbe.2017028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Altruism is typically associated with traits or behaviors that benefit the population as a whole, but are costly to the individual. We propose that, when the environment is rapidly changing, senescence (age-related deterioration) can be altruistic. According to numerical simulations of an agent-based model, while long-lived individuals can outcompete their short lived peers, populations composed of long-lived individuals are more likely to go extinct during periods of rapid environmental change. Moreover, as in many situations where other cooperative behavior arises, senescence can be stabilized in a structured population.
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Affiliation(s)
- Minette Herrera
- School of Mathematical and Natural Sciences, Arizona State University, Glendale, AZ 85306-4908, United States.
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9
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Cooperation and strategy coexistence in a tag-based multi-agent system with contingent mobility. Knowl Based Syst 2016. [DOI: 10.1016/j.knosys.2016.08.024] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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10
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Deng X, Zhang Q, Deng Y, Wang Z. A novel framework of classical and quantum prisoner's dilemma games on coupled networks. Sci Rep 2016; 6:23024. [PMID: 26975447 PMCID: PMC4792163 DOI: 10.1038/srep23024] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2015] [Accepted: 02/22/2016] [Indexed: 11/16/2022] Open
Abstract
Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. To mimick two kinds of different interactive environments and mechanisms, in this paper a new framework of classical and quantum prisoner's dilemma games on two-layer coupled networks is considered. Within the proposed model, the impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Simulation results show that the entanglement has no impact on the evolution of the classical prisoner's dilemma, while the rise of the coupling factor obviously impedes cooperation in this game, and the evolution of quantum prisoner's dilemma is greatly impacted by the combined effect of entanglement and coupling.
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Affiliation(s)
- Xinyang Deng
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
- Center for Quantitative Sciences, Vanderbilt University School of Medicine, Nashville, TN, 37232, USA
| | - Qi Zhang
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
| | - Yong Deng
- School of Computer and Information Science, Southwest University, Chongqing, 400715, China
- Big Data Decision Institute, Jinan University, Tianhe, Guangzhou, 510632, China
| | - Zhen Wang
- School of Automation, Northwestern Polytechnical University, Xi’an, 710072, China
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11
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Decision-Making in Agent-Based Models of Migration: State of the Art and Challenges. EUROPEAN JOURNAL OF POPULATION-REVUE EUROPEENNE DE DEMOGRAPHIE 2016; 32:73-97. [PMID: 27069292 PMCID: PMC4803816 DOI: 10.1007/s10680-015-9362-0] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/04/2014] [Accepted: 07/25/2015] [Indexed: 11/29/2022]
Abstract
We review agent-based models (ABM) of human migration with respect to their decision-making rules. The most prominent behavioural theories used as decision rules are the random utility theory, as implemented in the discrete choice model, and the theory of planned behaviour. We identify the critical choices that must be made in developing an ABM, namely the modelling of decision processes and social networks. We also discuss two challenges that hamper the widespread use of ABM in the study of migration and, more broadly, demography and the social sciences: (a) the choice and the operationalisation of a behavioural theory (decision-making and social interaction) and (b) the selection of empirical evidence to validate the model. We offer advice on how these challenges might be overcome.
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12
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Zhang Y, Fu F, Chen X, Xie G, Wang L. Cooperation in group-structured populations with two layers of interactions. Sci Rep 2015; 5:17446. [PMID: 26632251 PMCID: PMC4668372 DOI: 10.1038/srep17446] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2015] [Accepted: 10/29/2015] [Indexed: 11/09/2022] Open
Abstract
Recently there has been a growing interest in studying multiplex networks where individuals are structured in multiple network layers. Previous agent-based simulations of games on multiplex networks reveal rich dynamics arising from interdependency of interactions along each network layer, yet there is little known about analytical conditions for cooperation to evolve thereof. Here we aim to tackle this issue by calculating the evolutionary dynamics of cooperation in group-structured populations with two layers of interactions. In our model, an individual is engaged in two layers of group interactions simultaneously and uses unrelated strategies across layers. Evolutionary competition of individuals is determined by the total payoffs accrued from two layers of interactions. We also consider migration which allows individuals to move to a new group within each layer. An approach combining the coalescence theory with the theory of random walks is established to overcome the analytical difficulty upon local migration. We obtain the exact results for all “isotropic” migration patterns, particularly for migration tuned with varying ranges. When the two layers use one game, the optimal migration ranges are proved identical across layers and become smaller as the migration probability grows.
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Affiliation(s)
- Yanling Zhang
- School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.,Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
| | - Feng Fu
- Theoretical Biology, Institute of Integrative Biology, ETH Zürich, 8092 Zürich, Switzerland
| | - Xiaojie Chen
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
| | - Guangming Xie
- Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
| | - Long Wang
- Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
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13
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Short-range mobility and the evolution of cooperation: an experimental study. Sci Rep 2015; 5:10282. [PMID: 25992715 PMCID: PMC4438713 DOI: 10.1038/srep10282] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2014] [Accepted: 03/26/2015] [Indexed: 11/09/2022] Open
Abstract
A pressing issue in biology and social sciences is to explain how cooperation emerges in a population of self-interested individuals. Theoretical models suggest that one such explanation may involve the possibility of changing one’s neighborhood by removing and creating connections to others, but this hypothesis has problems when random motion is considered and lacks experimental support. To address this, we have carried out experiments on diluted grids with human subjects playing a Prisoner’s Dilemma. In contrast to previous results on purposeful rewiring in relational networks, we have found no noticeable effect of mobility in space on the level of cooperation. Clusters of cooperators form momentarily but in a few rounds they dissolve as cooperators at the boundaries stop tolerating being cheated upon. Our results highlight the difficulties that mobile agents have to establish a cooperative environment in a spatial setting.
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14
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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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15
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Impact of roles assignation on heterogeneous populations in evolutionary dictator game. Sci Rep 2014; 4:6937. [PMID: 25377303 PMCID: PMC4223679 DOI: 10.1038/srep06937] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2013] [Accepted: 10/20/2014] [Indexed: 11/08/2022] Open
Abstract
The evolution of cooperation is a hot and challenging topic in the field of evolutionary game theory. Altruistic behavior, as a particular form of cooperation, has been widely studied by the ultimatum game but not by the dictator game, which provides a more elegant way to identify the altruistic component of behaviors. In this paper, the evolutionary dictator game is applied to model the real motivations of altruism. A degree-based regime is utilized to assess the impact of the assignation of roles on evolutionary outcome in populations of heterogeneous structure with two kinds of strategic updating mechanisms, which are based on Darwin's theory of evolution and punctuated equilibrium, respectively. The results show that the evolutionary outcome is affected by the role assignation and that this impact also depends on the strategic updating mechanisms, the function used to evaluate players' success, and the structure of populations.
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16
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Deng X, Wang Z, Liu Q, Deng Y, Mahadevan S. A belief-based evolutionarily stable strategy. J Theor Biol 2014; 361:81-6. [DOI: 10.1016/j.jtbi.2014.07.009] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2014] [Revised: 07/03/2014] [Accepted: 07/07/2014] [Indexed: 10/25/2022]
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17
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Vainstein MH, Brito C, Arenzon JJ. Percolation and cooperation with mobile agents: geometric and strategy clusters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:022132. [PMID: 25215713 DOI: 10.1103/physreve.90.022132] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2014] [Indexed: 06/03/2023]
Abstract
We study the conditions for persistent cooperation in an off-lattice model of mobile agents playing the Prisoner's Dilemma game with pure, unconditional strategies. Each agent has an exclusion radius r(P), which accounts for the population viscosity, and an interaction radius r(int), which defines the instantaneous contact network for the game dynamics. We show that, differently from the r(P)=0 case, the model with finite-sized agents presents a coexistence phase with both cooperators and defectors, besides the two absorbing phases, in which either cooperators or defectors dominate. We provide, in addition, a geometric interpretation of the transitions between phases. In analogy with lattice models, the geometric percolation of the contact network (i.e., irrespective of the strategy) enhances cooperation. More importantly, we show that the percolation of defectors is an essential condition for their survival. Differently from compact clusters of cooperators, isolated groups of defectors will eventually become extinct if not percolating, independently of their size.
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Affiliation(s)
- Mendeli H Vainstein
- Instituto de Física, Universidade Federal do Rio Grande do Sul, C.P. 15051, 91501-970 Porto Alegre RS, Brazil
| | - Carolina Brito
- Instituto de Física, Universidade Federal do Rio Grande do Sul, C.P. 15051, 91501-970 Porto Alegre RS, Brazil
| | - Jeferson J Arenzon
- Instituto de Física, Universidade Federal do Rio Grande do Sul, C.P. 15051, 91501-970 Porto Alegre RS, Brazil
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18
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Jin Q, Wang L, Xia CY, Wang Z. Spontaneous symmetry breaking in interdependent networked game. Sci Rep 2014; 4:4095. [PMID: 24526076 PMCID: PMC3924213 DOI: 10.1038/srep04095] [Citation(s) in RCA: 136] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2013] [Accepted: 01/23/2014] [Indexed: 11/09/2022] Open
Abstract
Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor α is smaller than a threshold value α(C), the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds α(C), spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method.
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Affiliation(s)
- Qing Jin
- Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115, USA
- School of Physics, Nankai University, Tianjin 300071, China
| | - Lin Wang
- Centre for Chaos and Complex Networks, Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong
| | - Cheng-Yi Xia
- Key Laboratory of Computer Vision and System (Ministry of Education) and Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300384, China
| | - Zhen Wang
- School of Physics, Nankai University, Tianjin 300071, China
- Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Center for Nonlinear Studies, Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex systems (Hong Kong), and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
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