Annals of Operations Research

, Volume 19, Issue 1, pp 435–446 | Cite as

Ascending bid auctions with behaviorally consistent bidders

  • Edi Karni
  • Zvi Safra
Part IV New Results In Nonlinear Preference Theory


Decision makers whose preferences do not satisfy the independence axiom of expected utility theory, when faced with sequential decisions will act in a dynamically inconsistent manner. In order to avoid this inconsistency and maintain nonexpected utility, we suggest the idea of behavioral consistency. We implement this notion by regarding the same decision maker at different decision nodes as different agents, and then taking the Bayesian — Nash equilibrium of this game. This idea is applied to a finite ascending bid auction game. We show the condition for the existence of an equilibrium of this game, and we also characterize the equilibrium in those cases when it exists. In particular, when the utility functionals are both quasi-concave and quasi-convex, then there is an equilibrium in dominant strategies where each bidder continues to bid if and only if the prevailing price is smaller than his value. In the case of quasi-concavity it is shown that, in equilibrium, each bidder has a value such that he continues with positive probability up to it, and withdraws after that.


Decision Maker Nash Equilibrium Nash Positive Probability Utility Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    S.H. Chew, A mixture set axiomatization of weighted utility theory, unpublished manuscript, University of Arizona (1981).Google Scholar
  2. [2]
    S.H. Chew, A generalization of the quasilinear mean with applications to the measurement of income inequality and decision theory resolving the Allais paradox, Econometrica 51(1983)1061.Google Scholar
  3. [3]
    S.H. Chew and K. MacCrimmon, Alpha-nu choice theory: A generalization of expected utility theory, unpublished manuscript, University of British Columbia (1979).Google Scholar
  4. [4]
    E. Dekel, An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom, Journal of Economic Theory 40(1986)304.Google Scholar
  5. [5]
    P.C. Fishburn, Transitive measurable utility, Journal of Economic Theory 31(1983)298.Google Scholar
  6. [6]
    J.W. Friedman, A non-cooperative equilibrium for supergames, Review of Economic Studies 113(1971)1.Google Scholar
  7. [7]
    I. Gilboa, Expected utility with purely subjective non-additive probabilities, Journal of Mathematical Economics 16(1987)65.Google Scholar
  8. [8]
    J. Harsanyi, Games with incomplete information played by Bayesian players, Parts I, II and III, Management Science 14(1967–8)159; 320; 486.Google Scholar
  9. [9]
    D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica 47(1979)263.Google Scholar
  10. [10]
    E. Karni and Z. Safra, Ascending bid auction games: A nonexpected utility analysis, Working Paper No. 20-87, The Foerder Institute for Economic Research, Tel-Aviv University (1987).Google Scholar
  11. [11]
    D.M. Kreps and R. Wilson, Sequential equilibria, Econometrica 50(1982)863.Google Scholar
  12. [12]
    M.J. Machina, “Expected utility” analysis without the independence axiom, Econometrica 50(1982)277.Google Scholar
  13. [13]
    B. Peleg and M. Yaari, On the existence of a consistent course of action when tastes are changing, Review of Economic Studies 40(1973)391.Google Scholar
  14. [14]
    J. Quiggin, A theory of anticipated utility, Journal of Economic Behavior and Organization 3(1982)324.Google Scholar
  15. [15]
    D. Schmeidler, Subjective probability and expected utility without additivity, Caress Working Paper No. 84-21, University of Pennsylvania (1984).Google Scholar
  16. [16]
    R. Selten, Re-examination of the perfectness concept for equilibrium points in extensive games, International Journal of Game Theory 4(1975)25.Google Scholar
  17. [17]
    R.H. Strotz, Myopia and inconsistency in dynamic utility maximization, Review of Economic Studies 23(1956)165.Google Scholar
  18. [18]
    M.E. Yaari, The dual theory of choice under risk, Econometrica 55(1987)95.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1989

Authors and Affiliations

  • Edi Karni
    • 1
  • Zvi Safra
    • 1
    • 2
  1. 1.Foerder Institute for Economic Research, Faculty of Social SciencesUniversity of Tel-AvivRamat AvivIsrael
  2. 2.The Johns Hopkins UniversityUSA

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