Abstract
In many social situations, individuals endeavor to find the single best possible partner, but are constrained to evaluate the candidates in sequence. Examples include the search for mates, economic partnerships, or any other long-term ties where the choice to interact involves two parties. Surprisingly, however, previous theoretical work on mutual choice problems focuses on finding equilibrium solutions, while ignoring the evolutionary dynamics of decisions. Empirically, this may be of high importance, as some equilibrium solutions can never be reached unless the population undergoes radical changes and a sufficient number of individuals change their decisions simultaneously. To address this question, we apply a mutual choice sequential search problem in an evolutionary game-theoretical model that allows one to find solutions that are favored by evolution. As an example, we study the influence of sequential search on the evolutionary dynamics of cooperation. For this, we focus on the classic snowdrift game and the prisoner’s dilemma game.
Highlights
The problem of mutual choice was first introduced in the economic literature by [1], who studied how to pair students with colleges so that the preference of both sides would be satisfied
We address this issue by embedding a mutual choice sequential search problem to an evolutionary game-theoretical framework, and look for decisions that are favored by evolution
We analyze the existence of strategies that are uninvadable or that can only be invaded by neutral drift
Summary
The problem of mutual choice was first introduced in the economic literature by [1], who studied how to pair students with colleges so that the preference of both sides would be satisfied. Even though previous work has explored various forms of optional interactions and partner choice, in the theory of the evolution of cooperation [25,26,27,28,29,30,31,32], trade-offs arising from sequential search problems have not been studied. We address this issue by embedding a mutual choice sequential search problem to an evolutionary game-theoretical framework, and look for decisions that are favored by evolution. If the search for new opponents is considered to be costly, high levels of cooperation may evolve even in the prisoner’s dilemma, where for obligatory interactions, defection yields the highest payoff This is because discriminated defectors have to on average search longer for an accepted interaction than cooperators and, pay higher costs associated with search. Mistakes in evaluating the type of opponent favor defection, because even if defectors are being discriminated against, they may be accepted by mistake
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