Symmetry breaking in the prisoner’s dilemma on two-layer dynamic multiplex networks

Takesue, Hirofumi

doi:10.1016/j.amc.2020.125543

Cited by 10 publications

(8 citation statements)

References 85 publications

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“…table 1) that represent the complex texture of relationships and model numerous layers that represent different social connections help cooperation endure even when the costs for exploitation are high [160]. Endogenous link updating in dynamic multiplex networks could lead to spontaneous symmetry breaking in cooperation levels across the layers [161][162][163].…”

Section: Network and Cooperationmentioning

confidence: 99%

Networks of reliable reputations and cooperation: a review

Takács

Gross

Testori

et al. 2021

Phil. Trans. R. Soc. B

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Reputation has been shown to provide an informal solution to the problem of cooperation in human societies. After reviewing models that connect reputations and cooperation, we address how reputation results from information exchange embedded in a social network that changes endogenously itself. Theoretical studies highlight that network topologies have different effects on the extent of cooperation, since they can foster or hinder the flow of reputational information. Subsequently, we review models and empirical studies that intend to grasp the coevolution of reputations, cooperation and social networks. We identify open questions in the literature concerning how networks affect the accuracy of reputations, the honesty of shared information and the spread of reputational information. Certain network topologies may facilitate biased beliefs and intergroup competition or in-group identity formation that could lead to high cooperation within but conflicts between different subgroups of a network. Our review covers theoretical, experimental and field studies across various disciplines that target these questions and could explain how the dynamics of interactions and reputations help or prevent the establishment and sustainability of cooperation in small- and large-scale societies. This article is part of the theme issue ‘The language of cooperation: reputation and honest signalling’.

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Section: Network and Cooperationmentioning

confidence: 99%

Networks of reliable reputations and cooperation: a review

Takács

Gross

Testori

et al. 2021

Phil. Trans. R. Soc. B

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“…In recent years multi-layered networks have attracted considerable attention to model multiple, simultaneous interactions within a single species (Gómez-Gardeñes et al, 2012b; Hayashi et al, 2016; Su et al, 2022). Collective behaviour in strategy updates can also support spontaneous symmetry breaking for certain connectivity structures, such as on lattices that can be divided into two sub-lattices (Szabó et al, 2010) or two-layer networks (Gómez-Gardeñes et al, 2012a; Jin et al, 2014; Lugo et al, 2020; Takesue, 2021).…”

Section: Discussionmentioning

confidence: 99%

Spontaneous symmetry breaking of cooperation between species

Hauert,

Szabó

2024

Preprint

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In mutualistic associations two species cooperate by exchanging goods or services with members of another species for their mutual benefit. At the same time competition for reproduction primarily continues with members of their own species. Inintra-species interactions the prisoner’s dilemma is the leading mathematical metaphor to study the evolution of cooperation. Here we considerinter-species interactions in the spatial prisoner’s dilemma, where members of each species reside on one lattice layer. Cooperators provide benefits to neighbouring members of the other species at a cost to themselves. Hence, interactions occur across layers but competition remains within layers. We show that rich and complex dynamics unfold when varying the cost-to-benefit ratio of cooperation,r. Four distinct dynamical domains emerge that are separated by critical phase transitions, each characterized by diverging fluctuations in the frequency of cooperation:(i)for largercooperation is too costly and defection dominates;(ii)for lowerrcooperators survive at equal frequencies in both species;(iii)loweringrfurther results in an intriguing, spontaneous symmetry breaking of cooperation between species with increasing asymmetry for decreasingr;(iv)finally, for smallr, bursts of mutual defection appear that increase in size with decreasingrand eventually drive the populations into absorbing states. Typically one species is cooperating and the other defecting and hence establish perfect asymmetry. Intriguingly and despite the symmetrical model setup, natural selection can nevertheless favour the spontaneous emergence of asymmetric evolutionary outcomes where, on average, one species exploits the other in a dynamical equilibrium.

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“…How to improve the level of cooperation and what methods can be used to better cooperate have attracted great attention in the academic community [4][5][6] . Under such background, evolutionary game theory [7][8][9] provides a good framework for explaining this phenomenon 10 , and results in many game models, such as prisoner's dilemma game [11][12][13] , snowdrift game [14][15][16] and ultimatum game 17,18 and public goods game 19,20 . In addition, a considerable number of mechanisms such as space and network [21][22][23] also play a very important role in promoting cooperation.…”

Section: Introductionmentioning

confidence: 99%

Prisoner’s Dilemma Game Model Based on Historical Strategy Information

Gou

2022

Preprint

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In many dilemmas, decisions are determined not by a single factor, but by multiple ones, including memory, reputation, reward and punishment, etc. In recent years, how to design a mechanism to promote cooperation has become a research hot-spot. However, most of the previous studies mainly consider the historical benefits of the game, and pay less attention to the stability of the strategy (that is, the frequency of strategy changes in the length of memory) and the proportion of memory in decision-making. The decision-making process of group evolution involves the influence of memory information on cooperative evolution in multi round games. It makes up for the lack of stability factors and weights in previous studies. Based on the above factors, a new strategy update rule is proposed to study the influence of the stability of historical strategy information on the evolution of cooperation in prisoner’s dilemma game, and the influence of memory weight on cooperation is considered. The stability of the current strategy is measured by the strategy in historical memory (the number of times the strategy in memory is continuous and consistent with the current strategy), which can determine the probability of an individual learning the neighbor strategy next time. Numerical simulation shows that an appropriate increase in the length of historical memory is more conducive to the emergence of cooperation, and the greater the weight of historical strategy information is, the more conducive to promoting cooperation, which shows that historical strategy information is still the main factor in decision-making. This study will help us understand the cooperative evolution of many real systems, such as nature, biology, society and so on, and effectively design reasonable mechanisms to promote cooperation.

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Symmetry breaking in the prisoner’s dilemma on two-layer dynamic multiplex networks

Cited by 10 publications

References 85 publications

Networks of reliable reputations and cooperation: a review

Networks of reliable reputations and cooperation: a review

Spontaneous symmetry breaking of cooperation between species

Prisoner’s Dilemma Game Model Based on Historical Strategy Information

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