Polymatrix games and optimization problems

Polymatrix games and optimization problems

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Article ID: iaor2014664
Volume: 75
Issue: 4
Start Page Number: 632
End Page Number: 645
Publication Date: Apr 2014
Journal: Automation and Remote Control
Authors: ,
Keywords: game theory, numerical analysis
Abstract:

Consideration was given to the properties of the polymatrix game, a finite noncooperative game of N players (N 3). A theorem of reduction of the search for Nash equilibria to an optimization problem was proved. This clears the way to the numerical search of equilibria. Additionally, a simple proof of the Nash theorem of existence of equilibrium in the polymatrix game was given using the theorem of existence of solution in the optimization problem.

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