Continuity of the payoff functions

被引：0
|
作者：
Dionysius Glycopantis
Allan Muir
机构：
[1] Department of Economics,
[2] City University,undefined
[3] Northampton Square,undefined
[4] London EC1V 0HB,undefined
[5] UK (e-mail: d.glycopantis@city.ac.uk),undefined
[6] Department of Mathematics,undefined
[7] City University,undefined
[8] Northampton Square,undefined
[9] London EC1V 0HB,undefined
[10] UK (e-mail: a.muir@city.ac.uk),undefined
来源：
Economic Theory | 2000年 / 16卷
关键词：
Keywords and Phrases: Payoff functions, Nash equilibrium, Weak topology, The Stone-Weierstrass Theorem.; JEL Classification Number:C72.;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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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页码：239 / 244
页数：5
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