Memory-based conformity enhances cooperation in social dilemmas

Abstract

The problem of how cooperative behaviors emerge in real world has been widely investigated and it is found that cooperative behaviors are closely related to memory, which means a rational player can get a more reasonable strategy by comprehensively considering certain amount of historical information within its memory scope. On the other hand, due to the potential risk during pursuing high payoff in human society, selecting the most common strategy for a player inside the interaction range is relatively safer, at least its payoff is not much lower than average, which is known as conformity. Motivated by these facts, we here propose a mechanism of conformity with memory whose core lies in two facts: (i) Each player first applies a memory rule to compare its own historical payoffs with a limited memory length and to take the strategy corresponding to the maximal payoff as historical optimal strategy; (ii) Each player can get the virtual optimal strategy by selecting the most common strategy from its neighbors’ historical optimal strategies according to the conformity rule. The asynchronous updating algorithm, together with the virtual strategy, is used to study the evolution of cooperation with different memory lengths on a regular lattice. Simulation results show that the proposed mechanism remarkably promotes cooperation in three classical evolutionary social dilemmas. More specifically, it is revealed that the cooperation level decreases gradually as the memory length increases in the prisoner’s dilemma and snowdrift game, and that the cooperation level increases as so does the memory length in the stag-hunt game.