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A Game-Theoretic Approach to the Binary Stochastic Choice Problem

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  • Itzhak Gilboa
  • Dov Monderer

Abstract

We provide an equivalence theorem for the binary stochastic choice problem, which may be thought of as an implicit characterization of binary choice probabilities which are consistent with a probability over linear orderings. In some cases this implicit characterization is very useful in derivation of explicit necessary conditions. In particular, we present a new set of conditions which generalizes both Cohen and Falmagne's and Fishburn's conditions.
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Suggested Citation

  • Itzhak Gilboa & Dov Monderer, 1989. "A Game-Theoretic Approach to the Binary Stochastic Choice Problem," Discussion Papers 854, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:854
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/854.pdf
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    References listed on IDEAS

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    1. Itzhak Gilboa, 1989. "A Necessary but Insufficient Condition for the Stochastic Binary Choice Problem," Discussion Papers 818, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Barbera, Salvador & Pattanaik, Prasanta K, 1986. "Falmagne and the Rationalizability of Stochastic Choices in Terms of Random Orderings," Econometrica, Econometric Society, vol. 54(3), pages 707-715, May.
    3. Gilboa, Itzhak & Monderer, Dov, 1991. "Quasi-values on Subspaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 353-363.
    4. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
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    1. Gilboa, Itzhak & Monderer, Dov, 1991. "Quasi-values on Subspaces," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 353-363.

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