Continuity of the payoff functions

Allan Muir () and Dionysius Glycopantis ()
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Allan Muir: Department of Mathematics, City University, Northampton Square, London EC1V 0HB, UK
Dionysius Glycopantis: Department of Economics, City University, Northampton Square, London EC1V 0HB, UK

Economic Theory, 2000, vol. 16, issue 1, 239-244

Abstract: In his Nash equilibrium paper, Glicksberg states that the payoff functions are continuous. Such a function is defined on the product of mixed strategies, which are the Borel probability measures on a compactum, endowed with the product of the weak topologies. The continuity property is used in proving the existence of Nash equilibria. This note proves that the payoff functions are continuous, which is not immediate to establish.

Keywords: Payoff functions; Nash equilibrium; Weak topology; The Stone-Weierstrass Theorem. (search for similar items in EconPapers)
Date: 2000-04-14
Note: Received: June 10, 1999; revised version: June 24, 1999
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Citations: View citations in EconPapers (2)

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