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

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  • 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.

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File URL: http://hermes-ir.lib.hit-u.ac.jp/rs/bitstream/10086/16956/1/070econDP07-02.pdf
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Bibliographic Info

Paper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2007-02.

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Length: 18 p.
Date of creation: Apr 2007
Date of revision:
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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Web page: http://www.econ.hit-u.ac.jp/
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Related research

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

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References

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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. Einy, Ezra & Haimanko, Ori & Moreno, Diego & Shitovitz, Benyamin, . "On the continuity of equilibrium and core correspondences in economies with differential information," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/288, Universidad Carlos III de Madrid.
  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. Atsushi Kajii & Stephen Morris, 1997. "Payoff Continuity in Incomplete Information Games," Discussion Papers 1193R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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.
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Cited by:
  1. Timothy Van Zandt & Kaifu Zhang, 2011. "A theorem of the maximin and applications to Bayesian zero-sum games," International Journal of Game Theory, Springer, vol. 40(2), pages 289-308, May.

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