Extended Proper Equilibrium

57 Pages Posted: 13 Sep 2017 Last revised: 21 Dec 2020

Date Written: December 20, 2020

Abstract

We introduce extended proper equilibrium, which refines proper equilibrium (Myerson, 1978) by adding across-player restrictions on trembles. This refinement coincides with proper equilibrium in games with two players but adds new restrictions in games with three or more players. One implication of these additional restrictions is that any tremble that is costless in equilibrium is regarded by all as more likely than any costly tremble, even one by a different player. At least one extended proper equilibrium exists in every finite game. The refinement can also be characterized in terms of a symmetric, meta-version of the game in which players originate from a common pool: if these players tremble symmetrically and in the way of proper equilibrium, then the induced play in the original game is an extended proper equilibrium.

Keywords: equilibrium refinement, trembles, extended proper equilibrium, proper equilibrium

JEL Classification: C72

Suggested Citation

Milgrom, Paul R. and Mollner, Joshua, Extended Proper Equilibrium (December 20, 2020). Available at SSRN: https://ssrn.com/abstract=3035565 or http://dx.doi.org/10.2139/ssrn.3035565

Paul R. Milgrom

Stanford University ( email )

Landau Economics Building
579 Serra Mall
Stanford, CA 94305-6072
United States
+1-650-723-3397 (Phone)
+1-419-791-8545 (Fax)

HOME PAGE: www.milgrom.net

Joshua Mollner (Contact Author)

Northwestern University - Kellogg School of Management ( email )

2211 Campus Drive
Evanston, IL 60208
United States

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