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Population Uncertainty and Poisson Games

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  • Roger B. Myerson

Abstract

A general class of models is developed for analyzing games with population uncertainty. Within this general class, a special class of Poisson games is defined. It is shown that Poisson games are uniquely characterized by properties of independent actions and enviornmental equivalence. The general definition of equilibrium for games with population uncertainty is formulated, and it is shown that the equilibria of Poisson games are invariant under payoff-irrelevant type splitting. An example of a large voting game is discussed, to illustrate the advantages of using a Poisson game model for large games.

Suggested Citation

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

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    1. Richard Engelbrecht-Wiggans, 1987. "On Optimal Reservation Prices in Auctions," Management Science, INFORMS, vol. 33(6), pages 763-770, June.
    2. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    3. John Ledyard, 1984. "The pure theory of large two-candidate elections," Public Choice, Springer, vol. 44(1), pages 7-41, January.
    4. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    5. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    6. 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.
    7. Thomas Palfrey & Howard Rosenthal, 1983. "A strategic calculus of voting," Public Choice, Springer, vol. 41(1), pages 7-53, January.
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