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Aspiration dynamics generate robust predictions in structured populations

Evolutionary game dynamics in structured populations are strongly affected by updating rules. Previous studies usually focus on imitation-based rules, which rely on payoff information of social peers. Recent behavioral experiments suggest that whether individuals use such social information for strategy updating may be crucial to the outcomes of social interactions. This hints at the importance of considering updating rules without dependence on social peers' payoff information, which, however, is rarely investigated. Here, we study aspiration-based self-evaluation rules, with which individuals self-assess the performance of strategies by comparing own payoffs with an imaginary value they aspire, called the aspiration level. We explore the fate of strategies on population structures represented by graphs or networks. Under weak selection, we analytically derive the condition for strategy dominance, which is found to coincide with the classical condition of risk-dominance. This condition holds for all networks and all distributions of aspiration levels, and for individualized ways of self-evaluation. Our condition can be intuitively interpreted: one strategy prevails over the other if the strategy brings more satisfaction to individuals than the other does. Our work thus sheds light on the intrinsic difference between evolutionary dynamics induced by aspiration-based and imitation-based rules.

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