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Volume 7, Issue 2, April 2018, Page: 11-19
Using a Two-Person Zero-Sum Game to Solve a Decision-Making Problem
Joseph Gogodze, Institute of Control System, Techinformi, Georgian Technical University, Tbilisi, Georgia
Received: May 30, 2018;       Accepted: Jun. 25, 2018;       Published: Jul. 17, 2018
Abstract
This study proposes a game-theoretic approach to solve a multiobjective decision-making problem. The essence of the method is that a normalized decision matrix can be considered as a payoff matrix for some zero-sum matrix game, in which the first player chooses an alternative and the second player chooses a criterion. Herein, the solution in mixed strategies of this game is used to construct a weighted sum of the primary criteria that leads to a solution of the primary multiobjective decision-making problem. The proposed method leads to a notionally objective weighting method for multiobjective decision-making and provides “true weights” even in the absence of preliminary subjective evaluations. The proposed new method has a simple application. It can be applied to decision-making problems with any number of alternatives/criteria, and its practical realization is limited only by the capabilities of the solver of the linear programming problem formulated to solve the corresponding zero-sum game. Moreover, as observed from the solutions of the illustrative examples, the results obtained with the proposed method are quite appropriate and competitive.
Keywords
Multiobjective Optimization, Decision-Making Problem, Two-Person Zero-Sum Matrix Game
Joseph Gogodze, Using a Two-Person Zero-Sum Game to Solve a Decision-Making Problem, Pure and Applied Mathematics Journal. Vol. 7, No. 2, 2018, pp. 11-19. doi: 10.11648/j.pamj.20180702.11
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