Coexistence of strategies and culturally-specific common knowledge: An evolutionary analysis

We analyze social dynamics in a continuous population where randomly matched individuals have to choose between two pure strategies only ('cooperate' (C) and 'not cooperate' (NC)). Individual payoffs associated with the possible outcomes of each interaction may differ across groups, depending on the specific social and cultural context to which each agent belongs. In particular, it is assumed that three sub-populations are initially present, 'framing' the game according to the prisoner's dilemma (PD), assurance game (AG) and other regarding (OR) payoff configurations, respectively. In other words, we assume that common knowledge about the payoffs of the game is 'culturally-specific'. In this context, we examine both the adoption process of strategies C and NC within each sub-population and the diffusion process of 'types' (PD, AG and OR) within the overall community. On the basis of an evolutionary game-theoretic approach, the paper focuses on the problem of coexistence of PD, AG and OR groups as well as of 'nice' (C) and 'mean' (NC) strategies. We show that coexistence between C and NC is possible in the heterogeneous community under examination, even if it is ruled out in homogeneous communities where only one of the three types is present.