An effective intervention algorithm for promoting cooperation in the prisoner’s dilemma game with multiple stable states

Abstract

Multiple stable states, hysteresis, sensitivity to initial distributions, and a control algorithm for promoting cooperation are studied in an evolutionary prisoner’s dilemma with agents connected into a regular random network. A system could evolve into states of different cooperative frequencies xc in different runs, even starting with the same initial cooperative frequency xc(in) and payoff parameters. For a large reward R, some values of xc(in) either take the system to a group of low cooperative frequency (LCF) states or to a few high cooperative frequency (HCF) states. These states differ by their network structures, with cooperative players connected into ring-like structure in LCF states and compact clusters in HCF states. Hysteresis in xc is observed when R is swept down and up, when the final state of the previous R is used as the initial state of the next R. The analysis led us to propose a closed pack cluster algorithm that gives HCF states effectively. The algorithm intervenes the system at some point in time by selectively switching some non-cooperative D-agents into cooperative C-agents at the peripheral of an existing cluster of C-agents. It ensures protection of a small C-cluster from which more cooperation can be induced. Practically, a governing body may first allow a society to evolve freely and then derive suitable policy to promote selected pockets of good practices for attaining a higher level of common good.