Selective attention to historical comparison or social comparison in the evolutionary iterated prisoner’s dilemma game

Abstract

This paper investigates an evolutionary iterated prisoner’s dilemma (IPD) model of multiple agents, in which agents interact in terms of the pair-wise IPD game while adapting their attitudes towards income stream risk. Specifically, agents will become more risk averse (or more risk seeking) if their game payoffs exceed (or fall below) their expectations. In particular, agents use their peers’ average payoffs as expectations (social comparison) when their payoffs are lower than their peers’ averages, but use their own historical payoffs as expectations (historical comparison) when their payoffs are higher than their peers’ averages. Such selective attention to social comparison or historical comparison manifests a desire for continuous improvement of agents. Simulations are conducted to investigate the evolution of cooperation under the selective attention mechanism. Results indicate that agents can sustain a highly cooperative equilibrium when they consider selective attention in adjusting their risk attitudes. This holds true for both the well-mixed and the network-based games, even in the presence of uncertain game payoffs. The reason is that, selective attention can significantly induce agents to adhere to conditional cooperation as well as to identify uncertainty in payoffs, which enhances the risk-averse behavior of agents in the IPD game. As a result, high levels of cooperation can be attained.