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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.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1189.

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Date of creation: Jun 1997
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Handle: RePEc:nwu:cmsems:1189

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  1. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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.
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  1. Poisson games in Wikipedia (English)

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