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

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