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A Neo2Bayesian Foundation of the Maximin Value for Two-Person Zero- Sum Games

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  • Hart, Sergiu
  • Modica, Salvatore
  • Schmeidler, David

Abstract

A joint derivation of utility and value for two-person zero-sum games is obtained using a decision theoretic approach. Acts map states to consequences. The latter are lotteries over prizes, and the set of states is a product of two finite sets (m rows and n columns). Preferences over acts are complete, transitive, continuous, monotonic and certainty-independent (Gilboa and Schmeidler (1989)), and satisfy a new axiom of strategic flexibility which we introduce. These axioms are shown to characterize preferences such that (i) the induced preferences on consequences are represented by a von Neumann-Morgenstern utility function, and (ii) each act is ranked according to the maxmin value of the corresponding m x n utility matrix (a two-person zero-sum game). An alternative statement of the result deals simultaneously with all finite two-person zero-sum games in the framework of conditional acts and preferences.

Suggested Citation

  • Hart, Sergiu & Modica, Salvatore & Schmeidler, David, 1990. "A Neo2Bayesian Foundation of the Maximin Value for Two-Person Zero- Sum Games," Foerder Institute for Economic Research Working Papers 275500, Tel-Aviv University > Foerder Institute for Economic Research.
    • Handle: RePEc:ags:isfiwp:275500
    DOI: 10.22004/ag.econ.275500
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    References listed on IDEAS

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    1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    2. R. J. Aumann & M. Maschler, 1972. "Some Thoughts on the Minimax Principle," Management Science, INFORMS, vol. 18(5-Part-2), pages 54-63, January.
    3. Karni, Edi & Schmeidler, David, 1990. "Utility Theory and Uncertainty," Foerder Institute for Economic Research Working Papers 275480, Tel-Aviv University > Foerder Institute for Economic Research.
    4. Tijs, S.H., 1981. "A characterization of the value of zero-sum two person games," Other publications TiSEM dc8d850f-f026-4f07-8049-1, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Frick, Mira & Iijima, Ryota & Le Yaouanq, Yves, 2019. "Boolean Representations of Preferences under Ambiguity," Rationality and Competition Discussion Paper Series 173, CRC TRR 190 Rationality and Competition.
    2. Maccheroni, Fabio & Marinacci, Massimo & Rustichini, Aldo, 2006. "Dynamic variational preferences," Journal of Economic Theory, Elsevier, vol. 128(1), pages 4-44, May.
    3. Brandl, Florian & Brandt, Felix, 2019. "Justifying optimal play via consistency," Theoretical Economics, Econometric Society, vol. 14(4), November.
    4. Mosquera, M.A. & Borm, P. & Fiestras-Janeiro, M.G. & García-Jurado, I. & Voorneveld, M., 2008. "Characterizing cautious choice," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 143-155, March.
    5. Mira Frick & Ryota Iijima & Yves Le Yaouanq, 2019. "Dispersed Behavior and Perceptions in Assortative Societies," Cowles Foundation Discussion Papers 2180, Cowles Foundation for Research in Economics, Yale University.

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