Population uncertainty and Poisson games

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 payoffirrelevant type splitting. An example of a large voting game is discussed, to illustrate the advantages of using a Poisson game model for large games. Acknowledgments. I have benefited from many discussions on this topic with John Hillas and Dov Samet. Support from the National Science Foundation grant SES-9308139 and from the Dispute Resolution Research Center is gratefully acknowledged. Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate * School of Management, Northwestern University, Evanston, IL 60208-2009. E-mail: [email protected] 1 POPULATION UNCERTAINTY AND POISSON GAMES by Roger B. Myerson