Economic Theory

, Volume 51, Issue 1, pp 1–12 | Cite as

An indistinguishability result on rationalizability under general preferences

Research Article

Abstract

In this paper, we show that, in the class of games where each player’s strategy space is compact Hausdorff and each player’s payoff function is continuous and “concave-like,” rationalizability in a variety of general preference models yields the unique set of outcomes of iterated strict dominance. The result implies that rationalizable strategic behavior in these preference models is observationally indistinguishable from that in the subjective expected utility model, in this class of games. Our indistinguishability result can be applied not only to mixed extensions of finite games, but also to other important applications in economics, for example, the Cournot–oligopoly model.

Keywords

Rationalizability Iterated dominance General preferences 

JEL Classification

C70 D82 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bergemann D., Morris S.: Strategic Distinguishability with an Application to Robust Virtual Implementation. Yale University, Mimeo (2007)Google Scholar
  2. Bergemann D., Morris S.: Robust virtual implementation. Theor Econ 4, 45–88 (2009)Google Scholar
  3. Bergemann D., Morris S., Takahashi S.: Interdependent Preferences and Strategic Distinguishability. Princeton University, Mimeo (2010)Google Scholar
  4. Bernheim B.D.: Rationalizable strategic behavior. Econometrica 52, 1007–1028 (1984)CrossRefGoogle Scholar
  5. Blume L., Brandenburger A., Dekel E.: Lexicographic probabilities and choice under uncertainty. Econometrica 59, 61–79 (1991)CrossRefGoogle Scholar
  6. Borgers T.: Pure strategy dominance. Econometrica 61, 423–430 (1993)CrossRefGoogle Scholar
  7. Chen Y.C., Long N.V., Luo X.: Iterated strict dominance in general games. Games Econ Behav 61, 299–315 (2007)CrossRefGoogle Scholar
  8. Daniëls T.: Pure strategy dominance with quasiconcave utility functions. Econ Bull 3, 1–8 (2008)Google Scholar
  9. Dow J., Werlang S.: Nash equilibrium under Knightian uncertainty: Breaking down backward induction. J Econ Theory 64, 305–324 (1994)CrossRefGoogle Scholar
  10. Dufwenberg M., Stegeman M.: Existence and uniqueness of maximal reductions under iterated strict dominance. Econometrica 70, 2007–2023 (2002)CrossRefGoogle Scholar
  11. Ely J.C.: Rationalizability and approximate common-knowledge. Northwestern University, Mimeo (2005)Google Scholar
  12. Epstein L.: Preference, rationalizability and equilibrium. J Econ Theory 73, 1–29 (1997)CrossRefGoogle Scholar
  13. Fan K.: Minimax theorems, Proc. Nat Acad Sci USA 39, 42–47 (1953)CrossRefGoogle Scholar
  14. Ghirardato P., Le Breton M.: Choquet rationality. J Econ Theory 90, 277–285 (2000)CrossRefGoogle Scholar
  15. Gilboa I., Schmeidler D.: Maxmin expected utility with non-unique prior. J Math Econ 18, 141–153 (1989)CrossRefGoogle Scholar
  16. Greenberg J., Gupta S., Luo X.: Mutually acceptable courses of action. Econ Theory 40, 91–112 (2009)CrossRefGoogle Scholar
  17. Hu T.W.: On p-rationalizability and approximate common certainty of rationality. J Econ Theory 136, 379–391 (2007)CrossRefGoogle Scholar
  18. Klibanoff K.: Uncertainty, Decision, and Normal-Form Games. Northwestern University, Mimeo (1996)Google Scholar
  19. Lo K.C.: Equilibrium in beliefs under uncertainty. J Econ Theory 71, 443–484 (1996)CrossRefGoogle Scholar
  20. Lo K.C.: Rationalizability and the savage axioms. Econ Theory 15, 727–733 (2000)CrossRefGoogle Scholar
  21. Luo X.: On the foundation of stability. Econ Theory 40, 185–201 (2009)CrossRefGoogle Scholar
  22. Machina M., Schmeidler D.: A more robust definition of subjective probability. Econometrica 60, 745–780 (1992)CrossRefGoogle Scholar
  23. Marinacci M.: Ambiguous games. Games Econ Behav 31, 191–219 (2000)CrossRefGoogle Scholar
  24. Moulin H.: Dominance solvability and Cournot stability. Math Soc Sci 7, 83–102 (1984)CrossRefGoogle Scholar
  25. Osborne M.J., Rubinstein A.: A Course in Game Theory. The MIT Press, MA (1994)Google Scholar
  26. Pearce D.: Rationalizable strategic behavior and the problem of perfection. Econometrica 52, 1029–1051 (1984)CrossRefGoogle Scholar
  27. Savage L.: The Foundations of Statistics. Wiley, NY (1954)Google Scholar
  28. Schmeidler D.: Subjective probability and expected utility without additivity. Econometrica 57, 571–587 (1989)CrossRefGoogle Scholar
  29. Sion M.: On general minimax theorems. Pacific J Math 8, 171–176 (1958)Google Scholar
  30. Tan T., Werlang S.: The Bayesian foundations of solution concepts of games. J Econ Theory 45, 370–391 (1988)CrossRefGoogle Scholar
  31. Weinstein, J., Yildiz, M.: Sensitivity of equilibrium behavior to higher-order beliefs in nice games. Games Econ Behav (2008). doi: 10.1016/j.geb.2010.07.003

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of EconomicsNational University of SingaporeSingaporeSingapore

Personalised recommendations