Subgame Perfect Equilibria and Communication in Stage Gamges

Alejandro Manelli ()
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Alejandro Manelli: W. P. Carey School of Business Department of Economics, http://wpcarey.asu.edu/Directory/stafffaculty.cfm?cobid=1039599

Working Papers from Department of Economics, W. P. Carey School of Business, Arizona State University

Abstract: Any stage-game with infinite choice sets can be approximated by finite games obtained as increasingly finer discretizations of the infinite game. The subgame perfect equilibrium outcomes of the finite games converge to a limit distribution. We prove that (i) if the limit distribution is feasible in the limit game, then it is also a subgame perfect equilibrium outcome of the limit game; and (ii) if the limit distribution prescribes sufficiently diffused behavior for first-stage players, then it is a subgame perfect equilibrium outcome of the limit game. These results are potentially useful in determining the existence of subgame perfect equilibria in applications. As an illustration of this potential, it is shown that the addition of cheap talk to the games considered restores the existence of subgame perfect equilibria.

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