Metastable Equilibria

42 Pages Posted: 11 May 2006

See all articles by Srihari Govindan

Srihari Govindan

University of Rochester

Robert Wilson

Stanford Graduate School of Business

Date Written: February 2006

Abstract

We define a refinement of Nash equilibria called metastability. This refinement supposes that the given game might be embedded within any global game that leaves its local bestreply correspondence unaffected. A selected set of equilibria is metastable if it is robust against perturbations of every such global game; viz., every sufficiently small perturbation of the best-reply correspondence of each global game has an equilibrium that projects arbitrarily near the selected set. Metastability satisfies the standard decision-theoretic axioms obtained by Mertens' (1989) refinement (the strongest proposed refinement), and it satisfies the projection property in Mertens' small-worlds axiom: a metastable set of a global game projects to a metastable set of a local game. But the converse is slightly weaker than Mertens' decomposition property: a metastable set of a local game contains a metastable set that is the projection of a metastable set of a global game. This is inevitable given our demonstration that metastability is equivalent to a strong form of homotopic essentiality. Mertens' definition invokes homological essentiality whereas we derive homotopic essentiality from primitives (robustness for every embedding). We argue that this weak version of decomposition has a natural gametheoretic interpretation.

Keywords: economic theory, game theory

JEL Classification: C72

Suggested Citation

Govindan, Srihari and Wilson, Robert B., Metastable Equilibria (February 2006). Stanford University Graduate School of Business Research Paper No. 1934, Available at SSRN: https://ssrn.com/abstract=900612 or http://dx.doi.org/10.2139/ssrn.900612

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)

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
88
Abstract Views
1,253
rank
319,298
PlumX Metrics