Theorem of the Maximin and Applications to Bayesian Zero-Sum Games

23 Pages Posted: 12 Feb 2010  

Kaifu Zhang

INSEAD

Timothy Van Zandt

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

Date Written: February 11, 2010

Abstract

Consider a family of zero-sum games indexed by a parameter that determines each player's payoff function and feasible strategies. Our first main result characterizes continuity assumptions on the payoffs and the constraint correspondence such that the equilibrium value and strategies depend continuously and upper hemicontinuously (respectively) on the parameter. This characterization uses two topologies in order to overcome a topological tension that arises when players' strategy sets are infinite-dimensional. Our second main result is an application to Bayesian zero-sum games in which each player's information is viewed as a parameter. We model each player's information as a sub-sigma-field, so that it determines her feasible strategies: those that are measurable with respect to the player's information. We thereby characterize conditions under which the equilibrium value and strategies depend continuously and upper hemicontinuously (respectively) on each player's information. This clarifies and extends related results of Einy et al. (2008).

Keywords: Value of Information, Zero-sum Games

Suggested Citation

Zhang, Kaifu and Van Zandt, Timothy, Theorem of the Maximin and Applications to Bayesian Zero-Sum Games (February 11, 2010). INSEAD Working Paper No. 2010/09/EPS/MKT. Available at SSRN: https://ssrn.com/abstract=1551352 or http://dx.doi.org/10.2139/ssrn.1551352

Kaifu Zhang

INSEAD ( email )

Boulevard de Constance
77305 Fontainebleau Cedex
France

Timothy Van Zandt (Contact Author)

Centre for Economic Policy Research (CEPR)

77 Bastwick Street
London, EC1V 3PZ
United Kingdom

INSEAD - Economics and Political Sciences ( email )

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

Paper statistics

Downloads
74
Rank
259,113
Abstract Views
531