Strategy equilibrium in dilemma games with off-diagonal payoff perturbations

Abstract

We analyze the strategy equilibrium of dilemma games considering a payoff matrix affected by small and random perturbations on the off-diagonal. Notably, a recent work [Proc. R. Soc. A 476, 20200116 (2020)] reported that while cooperation is sustained by perturbations acting on the main diagonal, a less clear scenario emerges when perturbations act on the off-diagonal. Thus, the second case represents the core of this investigation, aimed at completing the description of the effects that payoff perturbations have on the dynamics of evolutionary games. Our results, achieved by analyzing the proposed model under a variety of configurations as different update rules, suggest that off-diagonal perturbations actually constitute a nontrivial form of noise. In particular, the most interesting effects are detected near the phase transition, as perturbations tend to move the strategy distribution towards nonordered states of equilibrium, supporting cooperation when defection is pervading the population, and supporting defection in the opposite case. To conclude, we identified a form of noise that, under controlled conditions, could be used to enhance cooperation and greatly delay its extinction.

Social dilemmas in off-lattice populations

“…This observation can be modeled by assuming an interaction graph where players have limited and stable partners, which fact determines their potential fitness and the dynamical process in the applied topology [8,9,10]. As expected, this modification may change the system behavior significantly which was confirmed by thousands of research papers in the last two decades [11,12,13,14,15,16,17,18,19].…”

Statistics of the number of equilibria in random social dilemma evolutionary games with mutation

“…Our analysis has made use of suitable changes of variables, which expressed the probability densities in terms of area of certain domains. For future work, we plan to generalise our method to other approaches to studying random social dilemmas such as finite population dynamics and payoff disturbances [2,3,16,36], as well as to multi-player [21,27,33] and more complex social dilemma games such as the climate change and technological race interactions [14,35].…”

Statistics of the number of equilibria in random social dilemma evolutionary games with mutation

“…Our analysis has made use of suitable changes of variables, which expressed the probability densities in terms of area of certain domains. For future work, we plan to generalise our method to other approaches to studying random social dilemmas such as finite population dynamics and payoff disturbances [13,30,1,2], as well as to multi-player social dilemma games [23,28,18].…”