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Colnaghi M, Santos FP, Van Lange PAM, Balliet D. Adaptations to infer fitness interdependence promote the evolution of cooperation. Proc Natl Acad Sci U S A 2023; 120:e2312242120. [PMID: 38055736 PMCID: PMC10723045 DOI: 10.1073/pnas.2312242120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 10/30/2023] [Indexed: 12/08/2023] Open
Abstract
The evolution of cooperation is a major question in the biological and behavioral sciences. While most theoretical studies model cooperation in the context of an isolated interaction (e.g., a Prisoner's Dilemma), humans live in heterogeneous social environments, characterized by large variations in fitness interdependence-the extent to which one's fitness is affected by others. Theoretical and experimental work indicates that humans can infer, and respond to, variations in interdependence. In a heterogeneous ancestral environment, these psychological mechanisms to infer fitness interdependence could have provided a selective advantage, allowing individuals to maximize their fitness by deciding when and with whom to cooperate. Yet, to date, the link between cognitive inference, variation in fitness interdependence, and cooperation remains unclear. Here we introduce a theoretical framework to study the evolution of inference and cooperation in heterogeneous social environments, where individuals experience interactions with varying levels of corresponding interests. Using a combination of evolutionary game theory and agent-based modeling, we model the evolution of adaptive agents, who incur a cost to infer interdependence, in populations of fixed-behavior agents who always cooperate or defect. Our results indicate that natural selection could promote the evolution of psychological mechanisms to infer fitness interdependence, provided that there is enough variation in fitness interdependence to offset the cost of inference. Under certain conditions, the fixation of adaptive agents results in higher levels of cooperation. This depends crucially on the type of inference performed and the features of the interdependence landscape.
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Affiliation(s)
- Marco Colnaghi
- Department of Experimental and Applied Psychology, Institute for Brain and Behaviour Amsterdam, Vrije Universiteit Amsterdam, Amsterdam1081BT, The Netherlands
| | - Fernando P. Santos
- Informatics Institute, University of Amsterdam, Amsterdam1098XH, The Netherlands
| | - Paul A. M. Van Lange
- Department of Experimental and Applied Psychology, Institute for Brain and Behaviour Amsterdam, Vrije Universiteit Amsterdam, Amsterdam1081BT, The Netherlands
| | - Daniel Balliet
- Department of Experimental and Applied Psychology, Institute for Brain and Behaviour Amsterdam, Vrije Universiteit Amsterdam, Amsterdam1081BT, The Netherlands
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Wang SY, Yao X, Yang YM, Chen D, Wang RW, Xie FJ. Super-rational aspiration promotes cooperation in the asymmetric game with peer exit punishment and reward. Heliyon 2023; 9:e16729. [PMID: 37346327 PMCID: PMC10279827 DOI: 10.1016/j.heliyon.2023.e16729] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2022] [Revised: 05/19/2023] [Accepted: 05/25/2023] [Indexed: 06/23/2023] Open
Abstract
Super-rational aspiration induced strategy updating with exit rights has been considered in some previous studies, in which the players adjust strategies in line with their payoffs and aspirations, and they have access to exit the game. However, exit payoffs for exiting players are automatically allocated, which is clearly contrary to reality. In this study, evolutionary cooperation dynamics with super-rational aspiration and asymmetry in the Prisoner's Dilemma game is investigated, where exit payoffs are implemented by local peers. The results show that for different population structures, the asymmetry of the system is always contributive to the participation of the players. Furthermore, we show that under different exit payoffs, super-rationality and asymmetry are conductive to the evolution of cooperation.
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Affiliation(s)
- Si-Yi Wang
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
| | - Xin Yao
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
| | - Yi-Mei Yang
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Daniel Chen
- The High School Affiliated to Renmin University of China, Beijing, 100097, China
| | - Rui-Wu Wang
- School of Ecology and Environment, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Feng-Jie Xie
- School of Modern Posts, Xi’an University of Posts & Telecommunications, Xi’an, Shaanxi, 710061, China
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Alberto Javarone M, Di Antonio G, Valerio Vinci G, Pietronero L, Gola C. Evolutionary dynamics of sustainable blockchains. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0642] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022] Open
Abstract
The energy sustainability of blockchains, whose consensus protocol rests on the Proof-of-Work, nourishes a heated debate. The underlying issue lies in a highly energy-consuming process, defined as mining, required to validate crypto-asset transactions. Mining is the process of solving a cryptographic puzzle, incentivized by the possibility of gaining a reward. The higher the number of users performing mining, i.e. miners, the higher the overall electricity consumption of a blockchain. For that reason, mining constitutes a negative environmental externality. Here, we study whether miners’ interests can meet the collective need to curb energy consumption. To this end, we introduce the Crypto-Asset Game, namely a model based on the framework of Evolutionary Game Theory devised for studying the dynamics of a population whose agents can play as crypto-asset users or as miners. The proposed model, studied via numerical simulations, reveals a rich spectrum of possible steady states. Interestingly, by setting the miners’ reward in the function of the population size, agents reach a strategy profile that optimizes global energy consumption. To conclude, can a Proof-of-Work-based blockchain become energetically sustainable? Our results suggest that blockchain protocol parameters could have a relevant role in the global energy consumption of this technology.
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Affiliation(s)
- Marco Alberto Javarone
- Centro Ricerche Enrico Fermi, Rome, Italy
- Centre for Blockchain Technologies, University College London, London, UK
| | - Gabriele Di Antonio
- Centro Ricerche Enrico Fermi, Rome, Italy
- Istituto Superiore di Sanità, Rome, Italy
- Università degli Studi Roma Tre, Rome, Italy
| | - Gianni Valerio Vinci
- Istituto Superiore di Sanità, Rome, Italy
- Università Roma Tor Vergata, Rome, Italy
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Shi Z, Wei W, Li B, Li C, Li H, Zheng Z. Two-layer network model of public goods games with intervention and corruption. CHAOS (WOODBURY, N.Y.) 2022; 32:063138. [PMID: 35778150 DOI: 10.1063/5.0088493] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Accepted: 05/16/2022] [Indexed: 06/15/2023]
Abstract
Public goods games are widely used to model social dilemmas involving multiple agents. Though defection is the only rational choice for an individual in a public goods game, cooperative behavior is observed in a variety of social dilemmas, which is the subject of our research. Punishing defectors has been shown to be an effective mechanism for promoting cooperation, but it relies on the third-party umpire being fair. In this article, an umpire intervention model with corruption is proposed to explore the impact of corruption on punishment mechanisms. In our model, players and umpires operate in a multilayer network. The players play public goods games, which are overseen by umpires. Fair umpires punish defectors, whereas corrupt umpires take bribes from defectors rather than meting out a punishment. We separately explore the effects of the fraction of fair umpires ρ, the spatial distribution, and the fine cost α and bribe cost β. Our Monte Carlo simulation shows that the above factors have a significant impact on cooperation. Intervention by an umpire always improves social efficiency, even for an entirely corrupt system. Moreover, relatively developed systems can resist corruption. Staggered and centralized distributions always have opposite effects on cooperative behavior, and these effects depend on ρ and r. We also find that whether cooperators fully occupy the player layer depends only on whether β reaches a certain threshold.
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Affiliation(s)
- Zhenyu Shi
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
| | - Wei Wei
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
| | - Baifeng Li
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
| | - Chao Li
- Department of Mathematics and Computer Science, Hengshui University, Hengshui 053000, China
| | - Haibin Li
- Key Laboratory of Mathematics Informatics Behavioral Semantics, Ministry of Education, Beijing 100191, China
| | - Zhiming Zheng
- School of Mathematical Sciences, Beihang University, Beijing 100191, China
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Amaral MA, de Oliveira MM. Criticality and Griffiths phases in random games with quenched disorder. Phys Rev E 2022; 104:064102. [PMID: 35030882 DOI: 10.1103/physreve.104.064102] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 11/22/2021] [Indexed: 11/07/2022]
Abstract
The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use evolutionary game theory to model a scenario with randomly perturbed payoffs in a prisoner's dilemma game. The perception diversity is modeled by adding a zero-average random noise in the payoff entries and a Monte Carlo simulation is used to obtain the population dynamics. This payoff heterogeneity can promote and maintain cooperation in a competitive scenario where only defectors would survive otherwise. In this work, we give a step further, understanding the role of heterogeneity by investigating the effects of quenched disorder in the critical properties of random games. We observe that payoff fluctuations induce a very slow dynamic, making the cooperation decay behave as power laws with varying exponents, instead of the usual exponential decay after the critical point, showing the emergence of a Griffiths phase. We also find a symmetric Griffiths phase near the defector's extinction point when fluctuations are present, indicating that Griffiths phases may be frequent in evolutionary game dynamics and play a role in the coexistence of different strategies.
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Affiliation(s)
- Marco A Amaral
- Instituto de Artes, Humanidades e Ciências, Universidade Federal do Sul da Bahia, Teixeira de Freitas-BA, 45996-108 Brazil
| | - Marcelo M de Oliveira
- Departamento de Física e Matemática, Universidade Federal de São João del Rei, Ouro Branco-MG, 36420-000 Brazil
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Jeong W, Yu U. Critical phenomena and strategy ordering with hub centrality approach in the aspiration-based coordination game. CHAOS (WOODBURY, N.Y.) 2021; 31:093114. [PMID: 34598449 DOI: 10.1063/5.0064406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 08/24/2021] [Indexed: 06/13/2023]
Abstract
We study the coordination game with an aspiration-driven update rule in regular graphs and scale-free networks. We prove that the model coincides exactly with the Ising model and shows a phase transition at the critical selection noise when the aspiration level is zero. It is found that the critical selection noise decreases with clustering in random regular graphs. With a non-zero aspiration level, the model also exhibits a phase transition as long as the aspiration level is smaller than the degree of graphs. We also show that the critical exponents are independent of clustering and aspiration level to confirm that the coordination game belongs to the Ising universality class. As for scale-free networks, the effect of aspiration level on the order parameter at a low selection noise is examined. In model networks (the Barabási-Albert network and the Holme-Kim network), the order parameter abruptly decreases when the aspiration level is the same as the average degree of the network. In contrast, in real-world networks, the order parameter decreases gradually. We explain this difference by proposing the concepts of hub centrality and local hub. The histogram of hub centrality of real-world networks separates into two parts unlike model networks, and local hubs exist only in real-world networks. We conclude that the difference of network structures in model and real-world networks induces qualitatively different behavior in the coordination game.
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Affiliation(s)
- Wonhee Jeong
- Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea
| | - Unjong Yu
- Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea
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Szolnoki A, Chen X. Cooperation and competition between pair and multi-player social games in spatial populations. Sci Rep 2021; 11:12101. [PMID: 34103617 PMCID: PMC8187490 DOI: 10.1038/s41598-021-91532-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2021] [Accepted: 05/21/2021] [Indexed: 11/25/2022] Open
Abstract
The conflict between individual and collective interests is in the heart of every social dilemmas established by evolutionary game theory. We cannot avoid these conflicts but sometimes we may choose which interaction framework to use as a battlefield. For instance some people like to be part of a larger group while other persons prefer to interact in a more personalized, individual way. Both attitudes can be formulated via appropriately chosen traditional games. In particular, the prisoner's dilemma game is based on pair interaction while the public goods game represents multi-point interactions of group members. To reveal the possible advantage of a certain attitude we extend these models by allowing players not simply to change their strategies but also let them to vary their attitudes for a higher individual income. We show that both attitudes could be the winner at a specific parameter value. Interestingly, however, the subtle interplay between different states may result in a counterintuitive evolutionary outcome where the increase of the multiplication factor of public goods game drives the population to a fully defector state. We point out that the accompanying pattern formation can only be understood via the multipoint or multi-player interactions of different microscopic states where the vicinity of a particular state may influence the relation of two other competitors.
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Affiliation(s)
- Attila Szolnoki
- Centre for Energy Research, Institute of Technical Physics and Materials Science, P.O. Box 49, 1525, Budapest, Hungary.
| | - Xiaojie Chen
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China
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Flores LS, Fernandes HCM, Amaral MA, Vainstein MH. Symbiotic behaviour in the public goods game with altruistic punishment. J Theor Biol 2021; 524:110737. [PMID: 33930439 DOI: 10.1016/j.jtbi.2021.110737] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2020] [Revised: 04/12/2021] [Accepted: 04/23/2021] [Indexed: 11/29/2022]
Abstract
Finding ways to overcome the temptation to exploit one another is still a challenge in behavioural sciences. In the framework of evolutionary game theory, punishing strategies are frequently used to promote cooperation in competitive environments. Here, we introduce altruistic punishers in the spatial public goods game. This strategy acts as a cooperator in the absence of defectors, otherwise it will punish all defectors in their vicinity while bearing a cost to do so. We observe three distinct behaviours in our model: i) in the absence of punishers, cooperators (who don't punish defectors) are driven to extinction by defectors for most parameter values; ii) clusters of punishers thrive by sharing the punishment costs when these are low; iii) for higher punishment costs, punishers, when alone, are subject to exploitation but in the presence of cooperators can form a symbiotic spatial structure that benefits both. This last observation is our main finding since neither cooperation nor punishment alone can survive the defector strategy in this parameter region and the specificity of the symbiotic spatial configuration shows that lattice topology plays a central role in sustaining cooperation. Results were obtained by means of Monte Carlo simulations on a square lattice and subsequently confirmed by a pairwise comparison of different strategies' payoffs in diverse group compositions, leading to a phase diagram of the possible states.
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Affiliation(s)
- Lucas S Flores
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, CEP 91501-970 Porto Alegre - RS, Brazil
| | - Heitor C M Fernandes
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, CEP 91501-970 Porto Alegre - RS, Brazil.
| | - Marco A Amaral
- Instituto de Humanidades, Artes e Ciências, Universidade Federal do Sul da Bahia, CEP, 45638-000 Teixeira de Freitas - BA, Brazil
| | - Mendeli H Vainstein
- Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, CEP 91501-970 Porto Alegre - RS, Brazil.
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