Adv. Math. Econ. Volume 6, pp.39-53 (2004)
The compactness of Pr(K)
Dionysius Glycopantis, Allan Muir
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Department of Economics, City University, Northampton Square, London EC1V 0HB, UK Department of Mathematics, City University, Northampton Square, London EC1V 0HB, UK
- We prove the compactness of Pr(K), the set of Borel probability measures on a compactum K endowed with the weak* topology, without embedding this set in rca(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.