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Article

Characteristic Function of Maxmax Defensive-Equilibrium Representation for TU-Games with Strategies

by
Chenwei Liu
1,
Shuwen Xiang
2,1,* and
Yanlong Yang
1
1
School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
2
College of Mathematical and Information Science, Guiyang University, Guiyang 550005, China
*
Author to whom correspondence should be addressed.
Axioms 2023, 12(6), 521; https://doi.org/10.3390/axioms12060521
Submission received: 13 March 2023 / Revised: 22 May 2023 / Accepted: 22 May 2023 / Published: 25 May 2023
(This article belongs to the Special Issue Advances in Logic and Game Theory)
Review Reports Versions Notes

Abstract

In this paper, we propose a characteristic function of the maxmax defensive-equilibrium representation that maps every TU-game with strategies to a TU-game. This characteristic function is given by a two-step procedure in which each of any two complementary coalitions successively selects the equilibrium in a way that maximizes its utility. We then investigate the properties of this characteristic function and present the relations of the cores under three characteristic functions. Finally, as applications of our findings, we provide a firm production advertising game, a supply chain network game, a cost game with strategies, and a Cournot game.
Keywords: cooperative games; characteristic functions; TU-game with strategies; core cooperative games; characteristic functions; TU-game with strategies; core

Share and Cite

MDPI and ACS Style

Liu, C.; Xiang, S.; Yang, Y. Characteristic Function of Maxmax Defensive-Equilibrium Representation for TU-Games with Strategies. Axioms 2023, 12, 521. https://doi.org/10.3390/axioms12060521

AMA Style

Liu C, Xiang S, Yang Y. Characteristic Function of Maxmax Defensive-Equilibrium Representation for TU-Games with Strategies. Axioms. 2023; 12(6):521. https://doi.org/10.3390/axioms12060521

Chicago/Turabian Style

Liu, Chenwei, Shuwen Xiang, and Yanlong Yang. 2023. "Characteristic Function of Maxmax Defensive-Equilibrium Representation for TU-Games with Strategies" Axioms 12, no. 6: 521. https://doi.org/10.3390/axioms12060521

APA Style

Liu, C., Xiang, S., & Yang, Y. (2023). Characteristic Function of Maxmax Defensive-Equilibrium Representation for TU-Games with Strategies. Axioms, 12(6), 521. https://doi.org/10.3390/axioms12060521

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