Abstract

http://ssrn.com/abstract=1551352
 
 

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


Kaifu Zhang


INSEAD

Timothy Van Zandt


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

February 11, 2010

INSEAD Working Paper No. 2010/09/EPS/MKT

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).

Number of Pages in PDF File: 23

Keywords: Value of Information, Zero-sum Games

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Date posted: February 12, 2010  

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: http://ssrn.com/abstract=1551352 or http://dx.doi.org/10.2139/ssrn.1551352

Contact Information

Kaifu Zhang
INSEAD ( email )
Boulevard de Constance
77305 Fontainebleau Cedex
France
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)
77 Bastwick Street
London, EC1V 3PZ
United Kingdom
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