On Zermelo's theorem

Rabah Amir; Igor V. Evstigneev

doi:10.3934/jdg.2017011

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2017, Volume 4, Issue 3: 191-194. Doi: 10.3934/jdg.2017011

This issue Previous Article Next Article A note on differential games with Pareto-optimal NASH equilibria: Deterministic and stochastic models^†

On Zermelo's theorem

Rabah Amir^1, , and
Igor V. Evstigneev^2,

1.
Department of Economics, University of Iowa, Iowa City, IA 52242-1994, USA
2.
Department of Economics, University of Manchester, Oxford Road, Manchester, M13 9PL, UK

* Corresponding author
* Corresponding author

Received: January 31, 2017

Revised: January 31, 2017

Published: September 2017

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Abstract

A famous result in game theory known as Zermelo's theorem says that ''in chess either White can force a win, or Black can force a win, or both sides can force at least a draw". The present paper extends this result to the class of all finite-stage two-player games of complete information with alternating moves. It is shown that in any such game either the first player has a winning strategy, or the second player has a winning strategy, or both have unbeatable strategies.

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Mathematics Subject Classification: Primary: 91A44; Secondary: 91A46, 91A25.

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References

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