Economic Theory Bulletin

, Volume 3, Issue 2, pp 287–298 | Cite as

Ordinal dominance and risk aversion

Research Article

Abstract

We find that, for sufficiently risk-averse agents, strict dominance by pure or mixed actions coincides with dominance by pure actions in the sense of (Börgers in Econometrica 61(2):423–430, 1993), which, in turn, coincides with the classical notion of strict dominance by pure actions when preferences are asymmetric. Since risk aversion is a cardinal feature, all finite single-agent choice problems with ordinal preferences admit compatible utility functions which are sufficiently risk averse as to achieve equivalence between pure and mixed dominance. This result extends to some infinite environments.

Keywords

Rationalizability Dominance Risk aversion Ordinal preferences Revealed preferences 

JEL Classification

D81 C72 

References

  1. Bernheim, D.: Rationalizable strategic behavior. Econometrica 52(4), 1007–1028 (1984)MATHMathSciNetCrossRefGoogle Scholar
  2. Bohner, M., Gelles, G.M.: Risk aversion and risk vulnerability in the continuous and discrete case. Decis. Econ. Financ. 35(1), 1–28 (2012)MATHMathSciNetCrossRefGoogle Scholar
  3. Bonanno, G.: A syntactic approach to rationality in games with ordinal payoffs. In: Bonanno, G., Van Der Hoek, W., Wooldridge, M. (eds.) Logic and the foundatons of game and decision theory (LOFT 7), Texts in logic and games, vol. 3, pp 59–85. Amsterdam University Press (2008)Google Scholar
  4. Börgers, T.: Pure strategy dominance. Econometrica 61(2), 423–430 (1993)MATHMathSciNetCrossRefGoogle Scholar
  5. Chambers, C.P., Echenique, F., Shmaya, E.: General revealed preference theory, Social Science Working Paper 1332, California Institute of Technology (2010)Google Scholar
  6. Chen, Y., Luo, X.: An indistinguishability result on rationalizability under general preferences. Econ. Theory 51(1), 1–12 (2012)MathSciNetCrossRefGoogle Scholar
  7. Daniëls, T.: Pure strategy dominance with quasiconcave utility functions. Econ. Bull. 2008(3), 54–61 (2008)Google Scholar
  8. Epstein, L.G.: Preference, rationalizability and equilibrium. J. Econ. Theory 73(1), 1–29 (1997)MATHCrossRefGoogle Scholar
  9. Klibanoff, P.: Characterizing uncertainty aversion through preference for mixtures. Soc. Choice Welf. 18(2), 289–301 (2001)MATHMathSciNetCrossRefGoogle Scholar
  10. Ledyard, J.O.: The scope of the hypothesis of Bayesian equilibrium. J. Econ. Theory 39(1), 59–82 (1986)MATHMathSciNetCrossRefGoogle Scholar
  11. Lo, K.C.: Rationalizability and the Savage axioms. Econ. Theory 15(3), 727–733 (2000)MATHCrossRefGoogle Scholar
  12. Pearce, D.: Rationalizable strategic behavior and the problem of perfection. Econometrica 52(4), 1029–1050 (1984)MATHMathSciNetCrossRefGoogle Scholar
  13. Rockafellar, R.T.: Convex analysis, Princeton landmarks in mathematics and physics, vol. 28, Princeton University Press (1996)Google Scholar
  14. Wald, A.: An essentially complete class of admissible decision functions. Ann. Math. Stat. 18(4), 549–555 (1947)MATHMathSciNetCrossRefGoogle Scholar
  15. Weinstein, J.: The dependence of solution concepts on risk attitude, mimeo (2014)Google Scholar
  16. Zimper, A.: Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets. Econ. Bull. 3(7), 1–6 (2005)Google Scholar

Copyright information

© Society for the Advancement of Economic Theory 2014

Authors and Affiliations

  1. 1.The Pennsylvania State UniversityUniversity ParkUSA
  2. 2.The Pennsylvania State UniversityUniversity ParkUSA
  3. 3.National Research University Higher School of EconomicsMoscowRussia

Personalised recommendations