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A Semi-Infinite Game

A. L. Soyster

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Abstract

The ordinary finite, two-person, zero-sum game is completely defined by specifying an m × n game matrix A. The optimal strategies for both players, and the value of the game, can be obtained by solving a dual pair of linear programming problems. In this paper a semi-infinite game is defined; a semi-infinite game matrix has an infinite number of columns, i.e., the game is specified by a sequence of vectors {P j } ∈ R m . Optimal strategies and game values are shown to exist for the semi-infinite game by exploiting the relationship between these games and linear programming over cones.

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What this paper is about

The ordinary finite, two-person, zero-sum game is completely defined by specifying an m × n game matrix A. The optimal strategies for both players, and the value of the game, can be obtained by solving a dual pair of linear programming problems. In this paper a semi-infinite game is defined; a semi-infinite game matrix has an infinite number of columns, i.e., the game is specified by a sequence of vectors {P j } ∈ R m . Optimal strategies and game values are shown to exist for the semi-infinite game by exploiting the relationship between these games and linear programming over cones.

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OpenAlex reports 12 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The ordinary finite, two-person, zero-sum game is completely defined by specifying an m × n game matrix A. The optimal strategies for both players, and the value of the game, can be obtained by solving a dual pair of linear programming problems. In this paper a semi-infinite game is defined; a semi-infinite game matrix has an infinite number of columns, i.e., the game is specified by a sequence of vectors {P j } ∈ R m . Optimal strategies and game values are shown to exist for the semi-infinite game by exploiting the relationship between these games and linear programming over cones.

Key concepts: Example of a game without a value, Normal-form game, Repeated game, Sequential game, Mathematics, Sequence (biology), Zero-sum game, Combinatorial game theory

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