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evolutionary game theory, counterfactual learning, myopic updating, asymmetric games, social dilemmas, volunteer’sdilemma
Abstract:
Social behavior in human and animal populations can be studied as an evolutionary process.Individuals often make decisions between different strategies, and those strategies that yield afitness advantage tend to spread. Traditionally, much work in evolutionary game theory considerssymmetric games: individuals are assumed to have access to the same set of strategies, and theyexperience the same payoff consequences. As a result, they can learn more profitable strategies byimitation. However, interactions are oftentimes asymmetric. In that case, imitation may beinfeasible (because individuals differ in the strategies they are able to use), or it may be undesirable(because individuals differ in their incentives to use a strategy). Here, we consider an alternativelearning process which applies to arbitrary asymmetric games,introspection dynamics. Accordingto this dynamics, individuals regularly compare their present strategy to a randomly chosenalternative strategy. If the alternative strategy yields a payoff advantage, it is more likely adopted. Inthis work, we formalize introspection dynamics for pairwise games. We derive simple and explicitformulas for the abundance of each strategy over time and apply these results to severalwell-known social dilemmas. In particular, for the volunteer’s timing dilemma, we show that theplayer with the lowest cooperation cost learns to cooperate without delay.
