Cooperation guided by the coexistence of imitation dynamics and aspiration dynamics in structured populations

Abstract

In the framework of the evolutionary game theory, two fundamentally different mechanisms, the imitation process and the aspiration-driven dynamics, can be adopted by players to update their strategies. In the former case, individuals imitate the strategy of a more successful peer, while in the latter case individuals change their strategies based on a comparison of payoffs they collect in the game to their own aspiration levels. Here we explore how cooperation evolves for the coexistence of these two dynamics. Intriguingly, cooperation reaches its lowest level when a certain moderate fraction of individuals pick aspiration-level–driven rule while the others choose pairwise comparison rule. Furthermore, when individuals can adjust their update rules besides their strategies, either imitation dynamics or aspiration-driven dynamics will finally take over the entire population, and the stationary cooperation level is determined by the outcome of competition between these two dynamics. We find that appropriate synergetic effects and moderate aspiration level boost the fixation probability of aspiration-driven dynamics most effectively. Our work may be helpful in understanding the cooperative behavior induced by the coexistence of imitation dynamics and aspiration dynamics in the society.

Evolutionary dynamics of networked multi-person games: mixing opponent-aware and opponent-independent strategy decisions

“…Most existing studies in setting how individuals make strategic decisions, normally, take a homogeneous hypothesis that all agents update strategies in the same way [3,4,39,43]. Even if when consolidating two distinct decision modes, the heterogeneity is mainly concentrated on the onefold information source or decision manner [27][28][29][30]. Given the diversity and self-organization of individual interaction [18,31], however, it is not unreasonable to predict that both heterogeneities can dramatically affect the evolutionary outcomes.…”

“…For instance, aspirationbased rules can give rise to intrinsically different properties compared with imitation-based rules [15,24,25], and such an effect also holds between the death-birth rule and the birth-death rule [19,26]. In particular, the hybrid dynamics of mixing two or multiple decision-making rules [27][28][29][30] have attracted tremendous interest recently, given the diversity and heterogeneity of human interactions [18,31,32]. Due to a large number of potential combinations, a complete exploration of these systems is a highly difficult and even impossible task.…”

Cooperative Evolution Mechanism of Unmanned Swarm within the Framework of Public Goods Game

“…Furthermore, the generalized evolutionary game model can be simplified as Markov chain + strategy update rules in finite population, so the average abundance function is also closely related to the strategy update rules. By studying strategy update rules in the framework of evolutionary game theory, one can differentiate between imitation processes and aspiration-driven dynamics [38]. In the former case, individuals imitate the strategy of a more successful peer [39].…”

Effects of updating rules on the coevolving prisoner’s dilemma

“…In addition, the effect of the network structure on the evolution of cooperation was investigated in other networks, including random regular graphs [12], small world networks [13][14][15] and actual social networks [16][17][18]. Furthermore, the role of networks in resolving social dilemma was investigated in combination with other mechanisms, including voluntary participation [19,20], heterogeneous teaching activity [21][22][23], time scale for strategy updating [24][25][26], payoff aspiration [27][28][29], conformity [30][31][32] and punishment [33][34][35][36].…”