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Population Uncertainty and Poisson Games

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  • Roger B. Myerson

Abstract

A general class of games with population uncertainty is formulated to describe situations where the set of players is not common knowledge. Simplifying independent-actions and environmental-equilvalence conditions imply that the numbers of players of each type are independent Poisson random variables. Equilibria of such Poisson games are defined and proven to exist. Formulas for approximating the equilibria of large Poisson games are derived, and are applied to a voting game in which participation is costly. We review how the analysis of such voting games can become more complicated and unrealistic when the set of players is assumed to be known.

Suggested Citation

  • Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1102
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    References listed on IDEAS

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    1. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    2. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
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    4. John Ledyard, 1984. "The pure theory of large two-candidate elections," Public Choice, Springer, vol. 44(1), pages 7-41, January.
    5. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    6. Richard Engelbrecht-Wiggans, 1987. "On Optimal Reservation Prices in Auctions," Management Science, INFORMS, vol. 33(6), pages 763-770, June.
    7. Palfrey, Thomas R. & Rosenthal, Howard, 1985. "Voter Participation and Strategic Uncertainty," American Political Science Review, Cambridge University Press, vol. 79(1), pages 62-78, March.
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