TY - JOUR

T1 - Decision analysis of rationalizable strategies in non-zero-sum multi-payoff games

AU - Eisenstadt-Matalon, Erella

AU - Moshaiov, Amiram

N1 - Publisher Copyright:
© 2022-IOS Press. All rights reserved.

PY - 2022/8/22

Y1 - 2022/8/22

N2 - 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).

AB - 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).

KW - Strategy selection

KW - multi-payoff game

KW - rationalizability

KW - strategy performance trade-off

KW - worst-case optimization

UR - http://www.scopus.com/inward/record.url?scp=85140835858&partnerID=8YFLogxK

U2 - 10.3233/IDT-210209

DO - 10.3233/IDT-210209

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AN - SCOPUS:85140835858

SN - 1872-4981

VL - 16

SP - 487

EP - 504

JO - Intelligent Decision Technologies

JF - Intelligent Decision Technologies

IS - 3

ER -