Interim Bayesian Nash Equilibrium on Universal Type Spaces for Supermodular Games

23 Pages Posted: 20 Nov 2007

See all articles by Timothy Van Zandt

Timothy Van Zandt

INSEAD - Economics and Political Sciences; Centre for Economic Policy Research (CEPR)

Date Written: March 2007

Abstract

We prove the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information. There are two main differences from the earlier proofs in Vives (1990) and Milgrom and Roberts (1990): we use the interim formulation of a Bayesian game, in which each player's beliefs are part of his or her type rather than being derived from a prior; we use the interim formulation of a Bayesian Nash equilibrium, in which each player and every type (rather than almost every type) chooses a best response to the strategy profile of the other players. Given also the mild restrictions on the type spaces, we have a proof of interim Bayesian Nash equilibrium for universal type spaces (for the class of supermodular utilities), as constructed, for example, by Mertens and Zami (1985)? We also weaken restrictions on the set of actions.

Keywords: Supermodular games, incomplete information, universal type spaces, interim Bayesian Nash equilibrium

Suggested Citation

Van Zandt, Timothy, Interim Bayesian Nash Equilibrium on Universal Type Spaces for Supermodular Games (March 2007). INSEAD Business School Research Paper No. 2007/14/EPS. Available at SSRN: https://ssrn.com/abstract=1031165 or http://dx.doi.org/10.2139/ssrn.1031165

Timothy Van Zandt (Contact Author)

INSEAD - Economics and Political Sciences ( email )

Boulevard de Constance
F-77305 Fontainebleau Cedex
France
+33 1 6072 4981 (Phone)
+33 1 6074 6192 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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