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.
Highlights
Animal Dispersion in Relation to Social Behavior was published by Wynne-Edwards and looked at the “Evolution of cooperation” [1]
Motivated by the abovementioned discussion, through combining direct reciprocity, indirect reciprocity, tag-based donation, and optimal control theory, a tag-based control (TBC) is proposed. e goal of this paper is to study the feasibility of promoting cooperation by TBC and designing an appropriate identified rate for operators
We show that an operator can design an optimal timing control (OTC) to optimize the control costs, the cooperation rate, and the cooperator’s payoff
Summary
Animal Dispersion in Relation to Social Behavior was published by Wynne-Edwards and looked at the “Evolution of cooperation” [1]. Axelrod and Hamilton proposed a model of the evolution of cooperation based on the iterated Prisoner’s Dilemma [11]. From the perspective of evolutionary games, the following objectives, inter alia, have been achieved through the designing of the control law: optimizing individual cost function [39], designing consensus control of stochastic multiagent systems [41], and promoting the evolution of cooperation in social dilemmas [23, 38]. (1) For the first time, a TBC that promotes the evolution of cooperation in the Prisoner’s Dilemma is proposed. We provide some concluding remarks and discussion in the last section
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