Affiliations: [a] Department of Mechanical Engineering, ORT Braude College of Engineering, Karmiel, Israel | [b] School of Mechanical Engineering, Tel-Aviv University, Tel-Aviv, Israel | [c] Sagol School of Neuroscience, Tel Aviv University, Tel-Aviv, Israel
Correspondence:
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Corresponding author: Erella Eisenstadt-Matalon, Department of Mechanical Engineering, ORT Braude College of Engineering, Karmiel, Israel. E-mail: [email protected].
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).
