Continuity of the payoff functions

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.

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Year of publication:	2000-04-14
Authors:	Muir, Allan ; Glycopantis, Dionysius
Published in:	Economic Theory. - Springer. - Vol. 16.2000, 1, p. 239-244
Publisher:	Springer
Subject:	Payoff functions \| Nash equilibrium \| Weak topology \| The Stone-Weierstrass Theorem

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Extent:	application/pdf
Type of publication:	Article
Notes:	Received: June 10, 1999; revised version: June 24, 1999
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005370717