Dynamic instabilities induced by asymmetric influence: Prisoners’ dilemma game in small-world networks

Kim, Beom Jun; Trusina, Ala; Holme, Petter; Minnhagen, Petter; Chung, Jean S.; Choi, M. Y.

doi:10.1103/physreve.66.021907

Cited by 212 publications

(133 citation statements)

References 19 publications

(10 reference statements)

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“…These spatial games, where the interactions are localized and non random, have been studied and extended in many ways (see, for example, Refs. [1,2,4,9,10,15,19,22,23,24,25,29,30,31,34,37,38,40,41,44,45,46,47,49,52]). Once the population is spatially structured, a natural question concerns the effects of mobility that, along with other important biological factors, is often neglected [28]: is it possible to evolve and sustain cooperation in a population of mobile agents, where retaliation can be avoided by moving away from the former partner?…”

Section: Introductionmentioning

confidence: 99%

Does mobility decrease cooperation?

Vainstein

Silva

Arenzon

2007

Journal of Theoretical Biology

274

192

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We explore the minimal conditions for sustainable cooperation on a spatially distributed population of memoryless, unconditional strategies (cooperators and defectors) in presence of unbiased, non contingent mobility in the context of the Prisoner's Dilemma game. We find that cooperative behavior is not only possible but may even be enhanced by such an "always-move" rule, when compared with the strongly viscous ("never-move") case. In addition, mobility also increases the capability of cooperation to emerge and invade a population of defectors, what may have a fundamental role in the problem of the onset of cooperation.

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Section: Introductionmentioning

confidence: 99%

Does mobility decrease cooperation?

Vainstein

Silva

Arenzon

2007

Journal of Theoretical Biology

274

192

View full text Add to dashboard Cite

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“…Effects of entries in the payoff matrix and addition of noise have been examined on different types of two-dimensional lattices [19]. Other topology related topics, such as the role of an 'influential node' [20] and optional participation [21] have been examined as well. In essence, a vast number of possible topologies and formulations has been studied.…”

Section: Introductionmentioning

confidence: 99%

The prisoner’s dilemma on co-evolving networks under perfect rationality

Biely

Dragosits

Thurner

2007

Physica D: Nonlinear Phenomena

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“…Following the pioneering work of Nowak et al [7,8] the two-strategy spatial evolutionary PD games have already been studied by several authors using different evolutionary rules on a large class of backgrounds including social networks [11,12,13,14] (for a survey of lattice models see the papers [15,16,17] and further references therein). In the present paper our attention is focused on the effect of noise built into the dynamical rule.…”

mentioning

confidence: 99%

Phase diagrams for an evolutionary prisoner’s dilemma game on two-dimensional lattices

2005

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The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary Prisoner's Dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive. Using systematic Monte Carlo simulations and different levels of the generalized mean-field approximations we have determined the phase boundaries (critical points) separating the two phases on the plane of the temperature (noise) and temptation to choose defection. In the zero temperature limit this analysis suggests that the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs. 05.50.+q, 02.50.+Le, 87.23.Ge In the original (two-player and one-shot) Prisoner's Dilemma (PD) game [1, 2] the players should simultaneously choose between two options, called defection and cooperation. The selfish players wish to maximize their own income in the knowledge of payoffs dependent on their choices. The curiosity of PD game is hidden in the fact that the choice of defection yields higher income independently of the partner's choice. However, if both players choose defection then their individual income is lower than those obtained for mutual cooperation when the maximum total payoff is shared equally. The rational (intelligent) players cannot resolve this dilemma and both of them choose defection (this is the so-called Nashequilibrium in the PD game). At the same time we find many examples in the nature where the mutual cooperation (altruism, ethical norms, etc.) emerges spontaneously among the selfish individuals [3]. In the last decades several mechanisms (e.g., kin selection [4], application of retaliating strategies [5], and voluntary participation [6]) are reported which enforce the appearance of cooperation in the societies.The spatial versions [7,8] of the evolutionary PD games can explain the maintenance of cooperation for the iterated games with a limited range of interaction if the players follow one of the two simplest strategies. For the two simplest strategies, denoted shortly as D and C, the player choose always defection and cooperation, respectively. In the evolutionary games the players wish to maximize their total payoff, coming from PD games with the neighbors, by adopting one of the more successful strategies available in their neighborhood. This type of dynamics describes the behavior of the ecological systems controlled by the Darwinian selection [9,10].Following the pioneering work of Nowak et al. [7,8] the two-strategy spatial evolutionary PD games have already been studied by several authors using different evolutionary rules on a large class of backgrounds including social networks [11,12,13,14] (for a survey of lattice models see the papers [15,16,17] and further references therein). In the present paper our attention is focused on the effect of noise built into the dynamical rule. It is tur...

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Dynamic instabilities induced by asymmetric influence: Prisoners’ dilemma game in small-world networks

Cited by 212 publications

References 19 publications

Does mobility decrease cooperation?

Does mobility decrease cooperation?

The prisoner’s dilemma on co-evolving networks under perfect rationality

Phase diagrams for an evolutionary prisoner’s dilemma game on two-dimensional lattices

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