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Uniform Continuity of the Value of Zero-Sum Games with Differential Information

Author

Listed:
  • Einy, Ezra
  • Haimanko, Ori
  • Moreno, Diego
  • 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 semi-continuous when the information fields of players change (even with the weak topology on players' strategy sets), and is approximately lower semi-continuous.

Suggested Citation

  • Einy, Ezra & Haimanko, Ori & Moreno, Diego & Shitovitz, Benyamin, 2007. "Uniform Continuity of the Value of Zero-Sum Games with Differential Information," Discussion Papers 2007-02, Graduate School of Economics, Hitotsubashi University.
    • Handle: RePEc:hit:econdp:2007-02
    Note: Revised version of Discussion Paper # 04-04 of Monaster Center for Economic Research, Ben-Gurion University of the Negev.
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    References listed on IDEAS

    as
    1. Kajii, Atsushi & Morris, Stephen, 1998. "Payoff Continuity in Incomplete Information Games," Journal of Economic Theory, Elsevier, vol. 82(1), pages 267-276, September.
    2. Van Zandt, Timothy, 2002. "Information, measurability, and continuous behavior," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 293-309, November.
    3. 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.
    4. 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.
    5. Stinchcombe, Maxwell B., 1990. "Bayesian information topologies," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 233-253.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Zero-Sum Games; Differential Information; Value; Op-timal Strategies; Uniform Continuity;

    JEL classification:

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

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