The Evolution of Cooperation and Reward in a Corrupt Environment

Abstract

The maintenance of cooperative behaviors in many complex social systems has always been a great challenge. It has been suggested that costly punishment and reward can both facilitate the evolution of cooperation. Recent theoretical work, however, reveals that the positive role of centralized punishment in promoting cooperation has been challenged when violators can bribe centralized authorities to escape from sanctions. Naturally, the question arises as to how cooperation evolves when defectors can bribe rewarders for getting the reward. Here, we propose an evolutionary game theoretical model in which defectors can choose to bribe the rewarders probabilistically, and meanwhile rewarders will stochastically receive bribes from defectors in the public goods game. We theoretically study deterministic dynamics in infinite populations, and find that cooperators, defectors, and rewarders can coexist and the fraction of each strategist in the population remains unchanged in the coexistence state. Furthermore, we numerically investigate stochastic dynamics in finite populations, and reveal that cooperative behaviors can be maintained since the population can spend most of the time in the region where cooperators, defectors, and rewarders coexist.