The effects of heterogeneous interaction and risk attitude adaptation on the evolution of cooperation

This paper addresses the evolution of cooperation in a multi-agent system with agents interacting heterogeneously with each other based on the iterated prisoner's dilemma (IPD) game. The heterogeneity of interaction is defined in two models. First, agents in a network are restricted to interacting with only their neighbors (local interaction). Second, agents are allowed to adopt different IPD strategies against different opponents (discriminative interaction). These two heterogeneous interaction scenarios are different to the classical evolutionary game, in which each agent interacts with every other agent in the population by adopting the same strategy against all opponents. Moreover, agents adapt their risk attitudes while engaging in interactions. Agents with payoffs above (or below) their aspirations will become more risk averse (or risk seeking) in subsequent interactions, wherein risk is defined as the standard deviation of one-move payoffs in the IPD game. In simulation experiments with agents using only own historical payoffs as aspirations (historical comparison), we find that the whole population can achieve a high level of cooperation via the risk attitude adaptation mechanism, in the cases of either local or discriminative interaction models. Meanwhile, when agents use the population's average payoff as aspirations (social comparison) for adapting risk attitudes, the high level of cooperation can only be sustained in a portion of the population (i.e., partial cooperation). This finding also holds true in both of the heterogeneous scenarios. Considering that payoffs cannot be precisely estimated in a realistic IPD game, simulation experiments are also conducted with a Gaussian disturbance added to the game payoffs. The results reveal that partial cooperation in the population under social comparison is more robust to the variation in payoffs than the global cooperation under historical comparison.