Title: A technique to solve mixed strategy non-cooperative zero sum games with more than two players

Authors: Ranjan Kumar Gupta; Debdip Khan

Addresses: Department of Commerce and Management, West Bengal State University, Barasat, W.B., India ' Department of Business Administration, Burdwan Raj College, Burdwan, W.B., India

Abstract: In this paper, we have proposed a technique, capable of solving m × n mixed strategy zero sum games with more than two players. To the best of our knowledge, no such definite technique is available in the literature. This work shows how one N-persons non-cooperative zero-sum game can be represented in two-dimensional space and then can be expressed as a combination of N numbers of two persons zero sum game. Using the mixed strategies of the different players obtained from the solutions (by our developed GA) of those two persons zero sum games and taking the payoffs from the initial representation of the N-persons game, the values of the game from different player's point of view have been calculated (sum being zero). Finally, our proposed technique has been demonstrated with a few examples and sensitivity analyses have been done graphically to confirm the stability of our GA.

Keywords: game theory; N-persons mixed strategy game; two-dimensional representation; two persons zero sum game; genetic algorithm.

DOI: 10.1504/IJOR.2024.137131

International Journal of Operational Research, 2024 Vol.49 No.3, pp.385 - 402

Received: 25 Feb 2021
Accepted: 20 Jun 2021
Published online: 04 Mar 2024 *

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