On a Generalization of the Lemke–Howson Algorithm to Noncooperative N-Person Games

descriptionPublicationkeyboard_double_arrow_right Article 01 Jul 1971 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Applied Mathematics, volume 21, pages 73-79 (issn: 0036-1399, eissn: 1095-712X,

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Authors: Rosenmüller, J.;

doi: 10.1137/0121010

On a Generalization of the Lemke–Howson Algorithm to Noncooperative N-Person Games

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Abstract

In [1] it has been shown that the existence of equilibrium points in a bimatrix game can be proved without a fixed-point theorem. If the game is nondegenerated, the number of equilibrium points is odd and all equilibrium points are obtained by a computational procedure in finitely many steps.The purpose of this note is to show that nondegeneracy can be defined for general N-person games and that for such games also there exist an odd number of equilibrium points. The algorithm developed in [1] can be extended to nondegenerated games even for more than 2 players.

Keywords

Noncooperative games, \(n\)-person games, \(n>2\)

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