International Journal of Game Theory

, Volume 27, Issue 3, pp 375-392

Population uncertainty and Poisson games

  • Roger B. MyersonAffiliated withDepartment of Managerial Economics and Decision Sciences, J.L. Kellogg Graduate School of Management, Northwestern University, Evanston, IL 60208-2009, USA (e-mail: myerson@nwu.edu)

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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 environmental 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.

Key words: Population uncertainty Poisson distribution Bayesian games