Adv. Math. Econ. Volume 6, pp.39-53 (2004)

The compactness ofPr(K)Dionysius Glycopantis, Allan Muir

Department of Economics, City University, Northampton Square, London EC1V 0HB, UK Department of Mathematics, City University, Northampton Square, London EC1V 0HB, UK PDF style DVI style

- We prove the compactness of
Pr(K), the set of Borel probability measures on a compactumKendowed with the weak* topology, without embedding this set inrca(K), the space of regular, countably-additive, signed measures with their finite total variation as norm.Pr(K)can be extended to a convex, Hausdorff, linear topological space. Then Glicksberg's fixed point theorem is applied to prove the existence of Nash equilibria.

- Borel probability measures, weak* topology, compactness, payoff functions, reaction correspondences, Nash equilibrium, fixed point theorem.