Theorem

Zermelo's Theorem (Game Theory)

Game Theory

In any finite two-player game of perfect information with no possibility of a draw, one of the two players has a winning strategy; allowing draws, at least one player has a strategy guaranteeing at least a draw. Proved by Ernst Zermelo for chess-like games, it is the founding determinacy result of combinatorial game theory.

Facts

Statement

Zermelo's theorem states that in any finite two-player game of perfect information with alternating moves and no element of chance, if the game cannot end in a draw then one of the two players must have a winning strategy that forces a win. 1

Proof Year

1913 1

Classification

Statement Form

Existence Theorem 1

Connections

Source Zermelo's Theorem (Game Theory) (Wikipedia)

Sources

1. Zermelo's Theorem (Game Theory) (Wikipedia)

Wikimedia Foundation

Introduction
The theorem is named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913.
In Group: Equilibria, Bargaining and Cooperative Games, Article text
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which chance does not affect the decision making process.
Proved By: Ernst Zermelo, Lead
The theorem is named after Ernst Zermelo, a German mathematician and logician, who proved the theorem for the example game of chess in 1913.

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Zermelo's Theorem (Game Theory)

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