Topological essentiality in infinite games

Yonghui Zhou; Jian Yu; Long Wang

doi:10.3934/jimo.2012.8.179

Article Contents

2012, Volume 8, Issue 1: 179-187. Doi: 10.3934/jimo.2012.8.179

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Topological essentiality in infinite games

1.
School of Mathematics and Computer Science, Guizhou Normal University, Guizhou, Guiyang 550001
2.
Department of Mathematics, Guizhou Uniersity, Guizhou, Guiyang 550025
3.
Center for Systems and Control, College of Engineering, Peking University, Beijing 100871

Received: January 31, 2011

Revised: August 31, 2011

Published: December 2011

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Abstract

By constructing a corresponding Nash map, we prove that every infinite game with compact metrizable sets of strategies and continuous payoffs has such a topological essential component that contains a minimal payoff-wise essential set containing a stable set, and deduce that every topological essential equilibrium is payoff-wise essential and so is perfect.

Keywords:

Mathematics Subject Classification: Primary: 91A10, 60B10; Secondary: 46G12.

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