Decision analysis of rationalizable strategies in non-zero-sum multi-payoff games

Abstract

This paper concerns multi-criteria decision-making in a non-cooperative situation between two Decision Makers (DMs), where each of the DMs (players) has self-conflicting objectives. This situation is modeled as a non-zero-sum Multi-Objective Game (nzs-MOG). In the considered case, selecting a strategy depends on the objective preferences of the DM and the inherent uncertainty about the preferences of the other player. In contrast to traditional studies on such a situation, which fail to consider the strategies’ performance trade-offs, here a set of rationalizable strategies is revealed for each of the players and their associated performance trade-offs are exposed and analyzed. Obtaining these strategies is done by an extension of the (worst-case) rationalizability solution concept from zero-sum MOGs to the considered general case of nzs-MOGs. In view of the aforementioned uncertainty about the other player, evaluating the rationalizable strategies involves comparisons between sets of payoff vectors. This causes a difficulty, when trying to analyze the alternative strategies by traditionalmulti-criteria decision-analysis techniques in which each alternative solution is commonly associated with only one payoff vector. To circumvent this difficulty, a technique is suggested, which transforms the set of payoff vectors of each strategy into a representative vector. To demonstrate the proposed technique, a nzs-MOG is devised and strategy analysis and selection is demonstrated, for each of the players, using the Analytical Hierarchy Process (AHP).