On a Game Connected with the Wiener Process

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1969 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:Theory of Probability & Its Applications, volume 14, pages 701-704 (issn: 0040-585X, eissn: 1095-7219,

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Authors: Gusein-Zade, S. M.;

doi: 10.1137/1114088

On a Game Connected with the Wiener Process

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Abstract

Summary: The following zero-sum game is considered. Two persons are observing a trajectory of a Wiener process in a bounded closed region \(E\) with absorbing boundary in a Euclidean \(n\)-space. One of the players may interrupt the process in a closed region \(E_1\) the other in \(E_2\). If the process is stopped in a point \(x\), then the first player pays to the second one payment \(g(x)\). The existence of the payoff function and minimax strategies is proved.

Keywords

2-person games, operations research

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