Optimal Tag-Based Cooperation Control for the “Prisoner’s Dilemma”

Abstract

A long-standing problem in biology, economics, and social sciences is to understand the conditions required for the emergence and maintenance of cooperation in evolving populations. This paper investigates how to promote the evolution of cooperation in the Prisoner’s Dilemma game (PDG). Differing from previous approaches, we not only propose a tag-based control (TBC) mechanism but also look at how the evolution of cooperation by TBC can be successfully promoted. The effect of TBC on the evolutionary process of cooperation shows that it can both reduce the payoff of defectors and inhibit defection; although when the cooperation rate is high, TBC will also reduce the payoff of cooperators unless the identified rate of the TBC is large enough. An optimal timing control (OTC) of switched replicator dynamics is designed to consider the control costs, the cooperation rate at terminal time, and the cooperator’s payoff. The results show that the switching control (SC) between an optimal identified rate control of the TBC and no TBC can properly not only maintain a high cooperation rate but also greatly enhance the payoff of the cooperators. Our results provide valuable insights for some clusters, for example, logistics parks and government, to regard the decision to promote cooperation.

Evolution of cooperation and trust in an N-player social dilemma game with tags for migration decisions

“…We also analysed the distribution of different tags within each group. Figure 11 shows a histogram plot of the standard deviations of all tags' populations within each groups, for simulations with different numbers of tags (2,3,5). We can see from the plots that all tags were generally evenly distributed within different groups.…”

“…It can be difficult to build mutual trust among the members in a population because of the high cost of fully understanding and accurately knowing each other’s willingness to cooperate [ 3 ], and this can influence the evolution of cooperation [ 4 , 5 ]. Various biological and social mechanisms have been studied in the literature to remedy this, and one of the most popular is the tag-based mechanism.…”

“…For example, with a tag-mediated altruism model, Hadzibeganovic et al [11] showed that tags can be used as an indirect form of reciprocity, which can then promote cooperative behaviour. More recent examples of such mechanisms include simple cues such as smiles to embody information that influences pro-social behaviour in social interactions [12], a third party controller that observes the interactions and labels the agents as either cooperators or defectors [3], and a dynamic tag determined by the system age or strategy age [13].…”