Memory mechanism with weighting promotes cooperation in the evolutionary games

Memory normally plays an important role when investigating the collective behaviours in real world. Each rational player can get a more reasonable strategy by comprehensively considering certain amount of historical information within its memory scope. Motivated by the fact, we here propose a memory mechanism with weighting whose core lies in three aspects: (i) Each player applies a memory rule to compare its own historical accumulated payoffs inside the range of memory length and to take the maximal one and corresponding strategy as historical optimal accumulated payoff and historical optimal strategy; (ii) Each neighbour of a player is endowed with a weighting which is the ratio of historical optimal accumulated payoff of each neighbour to the total historical optimal accumulated payoff of all neighbours of the player; (iii) Each player interacts with a neighbour selected by probability equal to weighting, and then updates its historical optimal strategy according to Fermi function. The asynchronous updating algorithm is used to study the evolution of cooperation with different memory lengths on a regular lattice. Simulation results show that the proposed mechanism effectively promotes cooperation in three classical social dilemmas. Moreover, it is revealed that the cooperation level, by and large, increases first and then decreases 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.