Exit Option Induced by Win-Stay-Lose-Leave Rule Provides Another Route to Solve the Social Dilemma in Structured Populations - Shen, Chen; Du, Chunpeng; Mu, Chunjiang; Shi, Lei; Wang, Zhen (Frontiers in Physics, 2020)
Theoretical studies have shown that cooperation can be promoted by the so-called “network reciprocity,” where cooperation can coexist with defection via the compact cooperative clusters. However, such studies often assume that players have no chance to exit from the game even if the situation is extremely bad for them, which is in sharp contrast with the real-life situations. Here, we relax this assumption by giving players the right to choose between one of two states, active (participate in the game) and inactive (exit from the game). We define this assumption as win-stay-lose-leave rule. This new rule motivates a winner whose payoff is larger than the average payoff of its neighbors to stay in its current state, thus retains its current advantage compared to its neighbors. Conversely, a loser is pushed to leave from its current state which in turn increase its chance to obtain a higher payoff while in inactive state. Specifically, we incorporate exit cost into consideration by assuming that anyone who decides to exit from the game must pay a cost γ. Extensive numerical simulation show that if the exit cost is intermediate (neither too high or too small), a full cooperation plateau is achieved, where cooperation evolves with the support of enhanced network reciprocity. In fact, inactive players can only exist at the boundary of cooperative clusters, which creates a crucial buffer area for the endangered cooperators. As a consequence, the joint effect of this protective film composed of inactive players and cooperative clusters forms the foundation of enhanced network reciprocity.