Stochastic evolutionary dynamics resolve the Traveler's Dilemma

JOURNAL OF THEORETICAL BIOLOGY

卷:303

Article

Manapat, Michael L.^2,3  Rand, David G.^2,4,5  Pawlowitsch, Christina⁶  Nowak, Martin A.^1,2,7 

[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[2] Harvard Univ, Program Evolutionary Dynam, Cambridge, MA 02138 USA

[3] Harvard Univ, Sch Engn & Appl Sci, Cambridge, MA 02138 USA

[4] Harvard Univ, Dept Psychol, Cambridge, MA 02138 USA

[5] Harvard Univ, Sch Law, Berkman Ctr Internet & Soc, Cambridge, MA 02138 USA

[6] Ecole Econ Paris, F-75014 Paris, France

[7] Harvard Univ, Dept Organism & Evolutionary Biol, Cambridge, MA 02138 USA

关键词: Stochastic game theory;    Evolutionary game theory;    Evolutionary dynamics;    Evolution of cooperation;    Social dilemmas;   

DOI  :  10.1016/j.jtbi.2012.03.014

来源: Elsevier

【 摘 要 】

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 v(1) and v(2), where v(1) < v(2), then the player choosing v(1) receives v(1) + R and the player choosing v(2) receives v(1)-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. (C) 2012 Elsevier Ltd. All rights reserved.

【 授权许可】

Free