Stability and robustness analysis of cooperation cycles driven by destructive agents in finite populations

Abstract

The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity

“…If both players are rational and adhere to this, they both end up with a payoff that is lower than the one they would obtained if they had chosen to cooperate. Despite its simplicity, however, the iterated prisoner's dilemma game continues to inspire research across the social and natural sciences [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. If the ranking of the payoffs is changed, other social dilemmas, such as the snowdrift game for T > R > S > P , are obtained, which has also received substantial attention in the recent past [28][29][30][31][32][33][34].…”

From pairwise to group interactions in games of cyclic dominance

“…For example, cyclic dominance has been observed in public goods games with volunteering [15,16], peer punishment [15,17,18], pool punishment [19,20], and reward [21,22], but also in pairwise social dilemmas with coevolution [23,24] or with jokers [25]. The ample attention to the theoretical aspects of cyclical interactions is fueled by actual observations of such interactions in nature.…”

Cooperation driven by success-driven group formation

“…Several adequate suggestions have been made in the last decade which try to address the conflict of experiment and theory [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. One of these research directions assumed that more sophisticated strategies should be used, which go beyond the simplest unconditional cooperator and defector behaviors [22,23].…”