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Uniform continuity of the value of zero-sum games with differential information

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  • Einy, Ezra
  • Haimanko, Ori
  • Shitovitz, Benyamin

Abstract

We establish uniform continuity of the value for zero-sum games with differential information, when the distance between changing information fields of each player is measured by the Boylan (1971) pseudo-metric. We also show that the optimal strategy correspondence is upper semicontinuous when the information fields of players change, even with the weak topology on players' strategy sets.

Suggested Citation

  • Einy, Ezra & Haimanko, Ori & Shitovitz, Benyamin, 2004. "Uniform continuity of the value of zero-sum games with differential information," UC3M Working papers. Economics we041603, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:we041603
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    1. Van Zandt, Timothy, 2002. "Information, measurability, and continuous behavior," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 293-309, November.
    2. Ezra Einy & Ori Haimanko & Diego Moreno & Benyamin Shitovitz, 2005. "On the continuity of equilibrium and core correspondences in economies with differential information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 793-812, November.
    3. Cotter, Kevin D., 1986. "Similarity of information and behavior with a pointwise convergence topology," Journal of Mathematical Economics, Elsevier, vol. 15(1), pages 25-38, February.
    4. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
    5. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
    7. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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