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The evolution of fairness under an assortative matching rule in the ultimatum game

  • Yasuhiro Shirata


This paper studies how a matching rule affects the evolution of fairness in an ultimatum mini game. Gale et al. [1995] show that only selfish behaviour survives in the deterministic replicator dynamics under the random matching rule. In contrast, this paper shows that, under an assortative matching rule, the fair behaviour may survive at an asymptotically stable state.

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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 41 (2012)
Issue (Month): 1 (February)
Pages: 1-21

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Handle: RePEc:spr:jogath:v:41:y:2012:i:1:p:1-21
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  1. Vega-Redondo,Fernando, 2003. "Economics and the Theory of Games," Cambridge Books, Cambridge University Press, number 9780521775908.
  2. Mendes, Rute & van den Berg, Gerard J & Lindeboom, Maarten, 2007. "An empirical assessment of assortative matching in the labor market," Working Paper Series 2007:30, IFAU - Institute for Evaluation of Labour Market and Education Policy.
  3. Binmore,K. & McCarthy,J. & Ponti,G. & ..., 1999. "A backward induction experiment," Working papers 34, Wisconsin Madison - Social Systems.
  4. Shimer, R. & Smith, L., 1997. "Assortative Matching and Search," Working papers 97-2a, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
  6. T. Borgers & R. Sarin, 2010. "Learning Through Reinforcement and Replicator Dynamics," Levine's Working Paper Archive 380, David K. Levine.
  7. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
  8. repec:oup:restud:v:66:y:1999:i:2:p:363-93 is not listed on IDEAS
  9. Becker, Gary S, 1974. "A Theory of Marriage: Part II," Journal of Political Economy, University of Chicago Press, vol. 82(2), pages S11-S26, Part II, .
  10. Ernst Fehr & Klaus M. Schmidt, . "A Theory of Fairness, Competition and Cooperation," IEW - Working Papers 004, Institute for Empirical Research in Economics - University of Zurich.
  11. repec:oup:qjecon:v:114:y:1999:i:3:p:817-868 is not listed on IDEAS
  12. Alp E. Atakan, 2006. "Assortative Matching with Explicit Search Costs," Econometrica, Econometric Society, vol. 74(3), pages 667-680, 05.
  13. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-46, July-Aug..
  14. Samuelson, L. & Zhang, J., 1991. "Evolutionary Stability in Asymmetric Games," Papers 9132, Tilburg - Center for Economic Research.
  15. Cressman, R., 1997. "Local stability of smooth selection dynamics for normal form games," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 1-19, August.
  16. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
  17. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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