Stochastic evolutionary dynamics resolve the Traveler's Dilemma

Abstract

Behavior in social dilemmas is often inconsistent with the predictions of classical game theory: people (and a wide variety of other organisms) are more cooperative than might be expected. Here we consider behavior in one such social dilemma, the Traveler's Dilemma, that has received considerable attention in the economics literature but is little known among theoretical biologists. The rules of the game are as follows. Two players each choose a value between R and M, where 0<R<M. If the players choose the same value, both receive that amount. If the players choose different values v1 and v2, where v1<v2, then the player choosing v1 receives v1+R and the player choosing v2 receives v1−R. While the players would maximize their payoffs by both choosing the largest allowed value, M, the Nash equilibrium is to choose the smallest allowed value, R. In behavioral experiments, however, people generally choose values much larger than the minimum and the deviation from the expected equilibrium decreases with R. In this paper, we show that the cooperative behavior observed in the Traveler's Dilemma can be explained in an evolutionary framework. We study stochastic evolutionary dynamics in finite populations with varying intensity of selection and varying mutation rate. We derive analytic results showing that strategies choosing high values can be favored when selection is weak. More generally, selection favors strategies that choose high values if R is small (relative to M) and strategies that choose low values if R is large. Finally, we show that a two-parameter model involving the intensity of selection and the mutation rate can quantitatively reproduce data that from a Traveler's Dilemma experiment. These results demonstrate the power of evolutionary game theory for explaining human behavior in contexts that are challenging for standard economic game theory.