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Uniform Continuity of the Value of Zero-Sum Games with Differential Information

Graduate School of Economics, Hitotsubashi University, Naka 2-1, Kunitachi, Tokyo 186-8601, Japan, and Department of Economics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
Department of Economics, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
Departamento de Economia, Universidad Carlos III de Madrid, 28903 Getafe, Spain
Department of Economics, University of Haifa, Haifa 31905, Israel
einy{at}bgu.ac.il
orih{at}bgu.ac.il
dmoreno{at}eco.uc3m.es
binya{at}econ.haifa.ac.il

We establish uniform continuity of the value for zero-sum games with differential information, when the distance between changing information fields of each player is measured by the Boylan pseudometric. We also show that the optimal strategy correspondence is upper semicontinuous when the information fields of players change (even with the weak topology on players' strategy sets), and is approximately lower semicontinuous.

Key Words: zero-sum games; differential information; value; optimal strategies; uniform continuity
History: Received: January 14, 2007; revision received: October 29, 2007;