Dynamically generated cyclic dominance in spatial prisoner's dilemma games

TL;DR

This paper explores how time-dependent learning capacities in spatial prisoner's dilemma games lead to dynamic cyclic dominance and support cooperation through different mechanisms.

Contribution

It introduces a model with time-varying learning activity, revealing new mechanisms for maintaining cooperation and strategy diversity in spatial games.

Findings

Time decreasing learning activity supports cooperation by recovering cooperator domains.

Temporary restrained learning activity creates cyclic dominance between strategies.

Results are robust across different parameters and network structures.

Abstract

We have studied the impact of time-dependent learning capacities of players in the framework of spatial prisoner's dilemma game. In our model, this capacity of players may decrease or increase in time after strategy adoption according to a step-like function. We investigated both possibilities separately and observed significantly different mechanisms that form the stationary pattern of the system. The time decreasing learning activity helps cooperator domains to recover the possible intrude of defectors hence supports cooperation. In the other case the temporary restrained learning activity generates a cyclic dominance between defector and cooperator strategies, which helps to maintain the diversity of strategies via propagating waves. The results are robust and remain valid by changing payoff values, interaction graphs or functions characterizing time-dependence of learning activity. Our observations suggest that dynamically generated mechanisms may offer alternative ways to keep cooperators alive even at very larger temptation to defect.