Repeated prisoner's dilemma games in multi-player structured populations with crosstalk

Abstract

Crosstalk represents a ubiquitous phenomenon in which strategic moves made in one game can influence actions in another. Reiter et al. [1] first integrated crosstalk with the repeated prisoner's dilemma model in structured populations. We extend their strategic space from one-step reactive strategies that consider only the actions of the opponent to memory-one strategies that consider the actions of both parties. We explore the cooperation rate of some representative memory-one strategies in repeated prisoner's dilemma games for multi-player structured populations when crosstalk exists, and focus on finding evolutionarily stable strategies that are cooperative in the memory-one strategy space under the impact of crosstalk. Simulation results in the strategic dynamics show that appropriately forgiving defection is conducive to cooperative stability in the population when crosstalk exists. Specifically, for strategies that can promote cooperation, there is a mutual restriction between tolerating the behavior of both defecting (the focused player and his opponent both defecting, DD) and forgiving unilateral defecting (the focused player cooperating while his opponent defecting, CD). That is, a more forgiving behavior of CD requires a lower tolerance for DD, while a higher tolerance of DD requires a less forgiving behavior of CD. Notably, we find two effective strategies, namely, Win-Stay-Lose-Shift (WSLS) and Firm‑but-Fair (FBF) in the facilitation of cooperation in game dynamics with crosstalk. Moreover, we reveal that the structured population can better suppress the negative impact of crosstalk on cooperation. This investigation provides complementary insights into the interplay between strategic decision-making and the influence of crosstalk within the context of memory-one strategies.