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Research Article

Evolution of fairness in the one-shot anonymous Ultimatum Game

David G. Rand, Corina E. Tarnita, Hisashi Ohtsuki, and Martin A. Nowak
PNAS first published January 22, 2013; https://doi.org/10.1073/pnas.1214167110
David G. Rand
aProgram for Evolutionary Dynamics,
bDepartment of Psychology,
cDepartment of Psychology, Yale University, New Haven, CT 06520;
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Corina E. Tarnita
aProgram for Evolutionary Dynamics,
dSociety of Fellows, and
eDepartment of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544;
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Hisashi Ohtsuki
fDepartment of Evolutionary Studies of Biosystems, School of Advanced Sciences, The Graduate University for Advanced Studies, Hayama, Kanagawa 240-0193, Japan; and
gPrecursory Research for Embryonic Science and Technology, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
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Martin A. Nowak
aProgram for Evolutionary Dynamics,
Departments of hOrganismic and Evolutionary Biology and
iMathematics, Harvard University, Cambridge, MA 02139;
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  • For correspondence: martin_nowak@harvard.edu
  1. Edited by Kenneth Wachter, University of California, Berkeley, CA, and approved December 19, 2012 (received for review August 15, 2012)

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Abstract

Classical economic models assume that people are fully rational and selfish, while experiments often point to different conclusions. A canonical example is the Ultimatum Game: one player proposes a division of a sum of money between herself and a second player, who either accepts or rejects. Based on rational self-interest, responders should accept any nonzero offer and proposers should offer the smallest possible amount. Traditional, deterministic models of evolutionary game theory agree: in the one-shot anonymous Ultimatum Game, natural selection favors low offers and demands. Experiments instead show a preference for fairness: often responders reject low offers and proposers make higher offers than needed to avoid rejection. Here we show that using stochastic evolutionary game theory, where agents make mistakes when judging the payoffs and strategies of others, natural selection favors fairness. Across a range of parameters, the average strategy matches the observed behavior: proposers offer between 30% and 50%, and responders demand between 25% and 40%. Rejecting low offers increases relative payoff in pairwise competition between two strategies and is favored when selection is sufficiently weak. Offering more than you demand increases payoff when many strategies are present simultaneously and is favored when mutation is sufficiently high. We also perform a behavioral experiment and find empirical support for these theoretical findings: uncertainty about the success of others is associated with higher demands and offers; and inconsistency in the behavior of others is associated with higher offers but not predictive of demands. In an uncertain world, fairness finishes first.

  • cooperation
  • prosociality
  • stochastic dynamics

Footnotes

  • ↵1D.G.R. and C.E.T. contributed equally to this work.

  • ↵2Author to whom correspondence should be addressed. E-mail: martin_nowak{at}harvard.edu.
  • Author contributions: D.G.R., C.E.T., H.O., and M.A.N. designed research, performed research, analyzed data, and wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1214167110/-/DCSupplemental.

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Evolution of fairness
David G. Rand, Corina E. Tarnita, Hisashi Ohtsuki, Martin A. Nowak
Proceedings of the National Academy of Sciences Jan 2013, 201214167; DOI: 10.1073/pnas.1214167110

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Evolution of fairness
David G. Rand, Corina E. Tarnita, Hisashi Ohtsuki, Martin A. Nowak
Proceedings of the National Academy of Sciences Jan 2013, 201214167; DOI: 10.1073/pnas.1214167110
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