Stable Outcomes of Generic Games in Extensive Form

22 Pages Posted: 9 May 2006

See all articles by Srihari Govindan

Srihari Govindan

University of Rochester

Robert Wilson

Stanford Graduate School of Business

Date Written: April 2006

Abstract

Mertens' (1989) definition of stability for a game in strategic form is applied to a game in extensive form with perfect recall. If payoffs are generic then the outcomes of stable sets of equilibria defined via homological essentiality by Mertens coincide with those defined via homotopic essentiality. This implies that for such games various definitions of stability in terms of perturbations of players' strategies as in Mertens, or best-reply correspondences as in Hillas (1990), yield the same outcomes. In proving this result it is convenient, as a practical matter, to work with enabling strategies, which are like behavioral strategies, instead of mixed strategies. A corollary yields a computational test that usually suffices to identify the stable outcomes of such a game.

Keywords: economic theory, game theory, extensive form, generic, stableset, computation

JEL Classification: C72

Suggested Citation

Govindan, Srihari and Wilson, Robert B., Stable Outcomes of Generic Games in Extensive Form (April 2006). Stanford University Graduate School of Business Research Paper No. 1933 (R), Available at SSRN: https://ssrn.com/abstract=900185 or http://dx.doi.org/10.2139/ssrn.900185

Srihari Govindan

University of Rochester ( email )

Department of Economics
Rochester, NY NY 14627
United States
5852757214 (Phone)

Robert B. Wilson (Contact Author)

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States
650-723-8620 (Phone)
650-725-7979 (Fax)

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