Correlated asynchronous behavior updating with a mixed strategy system in spatial prisoner's dilemma games enhances cooperation

Highlights: • A new model for SPD, based on mixed strategy, correlated with neighbors' strategy is obtained. • We found that the dynamics can be featured with D-END and D-EXP periods. - Abstract: A new model of mixed strategy system for spatial prisoner's dilemma games is proposed. As an alternative to the typical mixed strategy system, wherein a behavior of either cooperation or defection is stochastically determined for each neighbor based on the agent's overall strategy, in our mixed strategy system, the agent instead correlates his strategies with those of his neighbors. For example, he tends to offer cooperation more frequently to his neighbor who is cooperative more often. This model provides results with significantly enhanced cooperation compared with those obtained with the conventional mixed strategy model. Interestingly, some of the evolutionary paths followed under strong dilemma situations can be divided into two specific periods: Defector-Enduring (D-END), when the number of defectors rapidly decreases, and the subsequent Defector-Expanding (D-EXP), when the surviving defectors' clusters start to expand, allowing the global cooperation fraction to fall to a lower level. The D-END and D-EXP periods seem analogous to the END and EXP periods presented by the author in previous studies.