Satoshi Kokubo

Universal scaling for the dilemma strength in evolutionary games.

Why would natural selection favor the prevalence of cooperation within the groups of selfish individuals? A fruitful framework to address this question is evolutionary game theory, the essence of which is captured in the so-called social dilemmas. Such dilemmas have sparked the development of a variety of mathematical approaches to assess the conditions under which cooperation evolves. Furthermore, borrowing from statistical physics and network science, the research of the evolutionary game dynamics has been enriched with phenomena such as pattern formation, equilibrium selection, and self-organization. Numerous advances in understanding the evolution of cooperative behavior over the last few decades have recently been distilled into five reciprocity mechanisms: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity. However, when social viscosity is introduced into a population via any of the reciprocity mechanisms, the existing scaling parameters for the dilemma strength do not yield a unique answer as to how the evolutionary dynamics should unfold. Motivated by this problem, we review the developments that led to the present state of affairs, highlight the accompanying pitfalls, and propose new universal scaling parameters for the dilemma strength. We prove universality by showing that the conditions for an ESS and the expressions for the internal equilibriums in an infinite, well-mixed population subjected to any of the five reciprocity mechanisms depend only on the new scaling parameters. A similar result is shown to hold for the fixation probability of the different strategies in a finite, well-mixed population. Furthermore, by means of numerical simulations, the same scaling parameters are shown to be effective even if the evolution of cooperation is considered on the spatial networks (with the exception of highly heterogeneous setups). We close the discussion by suggesting promising directions for future research including (i) how to handle the dilemma strength in the context of co-evolution and (ii) where to seek opportunities for applying the game theoretical approach with meaningful impact.

How is the equilibrium of continuous strategy game different from that of discrete strategy game

Cooperation in the prisoners dilemma (PD) played on various networks has been explained by so-called network reciprocity. Most of the previous studies presumed that players can offer either cooperation (C) or defection (D). This discrete strategy seems unrealistic in the real world, since actual provisions might not be discrete, but rather continuous. This paper studies the differences between continuous and discrete strategies in two aspects under the condition that the payoff function of the former is a linear interpolation of the payoff matrix of the latter. The first part of this paper proves theoretically that for two-player games, continuous and discrete strategies have different equilibria and game dynamics in a well-mixed but finite population. The second part, conducting a series of numerical experiments, reveals that such differences become considerably large in the case of PD games on networks. Furthermore, it shows, using the Wilcoxon sign-rank test, that continuous and discrete strategy games are statistically significantly different in terms of equilibria. Intensive discussion by comparing these two kinds of games elucidates that describing a strategy as a real number blunts D strategy invasion to C clusters on a network in the early stage of evolution. Thus, network reciprocity is enhanced by the continuous strategy.

Spatial reciprocity for discrete, continuous and mixed strategy setups

The existence of cooperation in the social dilemma has been extensively studied based on spatial structure populations, namely, the so-called spatial reciprocity. However, vast majority of existing works just simply presume that agents can offer the discrete choice: either the cooperative (C) or defective (D) strategy, which, to some extent, seems unrealistic in the empirical observations since actual options might be continuous, mixed rather than discrete. Here, we propose discrete, continuous and mixed strategy setups in the social dilemma games and further explore their performance on network populations. Interestingly, it is unveiled that there is actually considerable inconsistency in terms of equilibrium among different strategy games. Furthermore, we reveal how different cooperative arrangements among these three strategy setups can be established, depending on whether the presumed dilemma subclass is a boundary game between prisoners dilemma game and Chicken game or between prisoners dilemma game and Stag-Hunt game.

Does copy-resistance enhance cooperation in spatial prisoner's dilemma?

We propose a novel idea for the so-called pairwise-Fermi process by considering copy-resistance when an agent copies a neighbors strategy, which implies that the focal agent with relatively affluent payoff vis-a-vis social average might be negative to copy her neighbors strategy even if her payoff is less than the neighbors payoff. Simulation results reveal that this idea with a revised strategy adaptation process significantly enhances cooperation for prisoners dilemma games played on time-constant networks.

Network reciprocity on spatial prisoner's dilemma games by Continuous-binary strategy

For 2 × 2 games, especially the Spatial Prisoners Dilemma (SPD), most of the previous studies presumed that players can offer either cooperation (C) or defection (D), the so-called discrete strategy. In this paper, we define Continuous-binary strategy instead of discrete strategy. And a systematic series of numerical simulations reports that it enhances the network reciprocity for SPD. This new strategy is based on our previous finding that continuous and mixed strategy are robust in boundary games of Chicken and PD (BCH), and Stag Hunt and PD (BSH), respectively. The new strategy allows to put both advantages of continuous and mixed strategies on usual discrete strategy together in one model.