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Large Poisson Games

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  • Roger B. Myerson

Abstract

Existence of equilibria is proven for Poisson games with compact type sets and finite action sets. Then three theorems are introduced for characterizing limits of probabilities in Poisson games when the expected number of players becomes large. The magnitude theorem characterizes the rate at which probabilities of events go zero. The offset theorem characterizes the ratios of probabilites of events that differ by a finite additive translation. The hyperplane theorem estimates probabilites of hyperplane events. These theorems are applied to derive formulas for pivot probabilities in binary elections, and to analyze a voting game that was studied by Ledyard.

Suggested Citation

  • Roger B. Myerson, 1997. "Large Poisson Games," Discussion Papers 1189, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1189
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    References listed on IDEAS

    as
    1. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    2. Igal Milchtaich, 1997. "Random-Player Games," Discussion Papers 1178, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. 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.
    4. John Ledyard, 1984. "The pure theory of large two-candidate elections," Public Choice, Springer, vol. 44(1), pages 7-41, January.
    5. 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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