A Necessary and Sufficient Condition for Pareto-Optimal Security Strategies in Multicriteria Matrix Games

Ghose, D (1991) A Necessary and Sufficient Condition for Pareto-Optimal Security Strategies in Multicriteria Matrix Games. In: Journal of Optimization Theory and Applications, 68 (3). pp. 463-481.

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Abstract

In this paper, a scalar game is derived from a zero-sum Multicriteria matrix game, and it is proved that the solution of the new game with strictly positive secularization is a necessary and sufficient Condition for a strategy to be a Pareto-optimal security strategy (POSS) For one of the players in the original game. Proving does this that a certain set, which is the extension of the set of security level vectors in the criterion function space, is convex and polyhedral. It is also established that only a finite number of scalarizations are necessary to obtain all the POSS for a player. An example is included to illustrate the main steps in the proof.

Item Type:	Journal Article
Publication:	Journal of Optimization Theory and Applications
Publisher:	Springer Netherlands
Additional Information:	Copyright of this article belongs to Springer Netherlands.
Keywords:	Game theory;Multicriteria games;Games with vector payoffs;Pareto-optimal security strategies;Multicriteria optimization;Scalarization methods
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	18 Sep 2006
Last Modified:	19 Sep 2010 04:31
URI:	http://eprints.iisc.ac.in/id/eprint/8484

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