On Coalitional Rationality in a Three-Person Game
- Authors: Zhukovskiy V.I1, Zhukovskaya L.V2, Smirnova L.V3, Vysokos M.I3
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Affiliations:
- Moscow State University
- Central Economics and Mathematics Institute, Russian Academy of Sciences
- State University of Humanities and Technology
- Issue: No 1 (2025)
- Pages: 40-45
- Section: Control in Social and Economic Systems
- URL: https://journal-vniispk.ru/1819-3161/article/view/351156
- ID: 351156
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Abstract
To determine the solution of any game in mathematical game theory, it is necessary to establish what behavior of the players should be considered optimal. In noncooperative games (games without coalitions), the concept of optimality is related, e.g., to the concepts of Nash and Berge equilibria. Optimality in the theory of cooperative games is characterized by the conditions of individual and collective rationality. This paper considers a three-person cooperative game in normal form. For this game, the concept of coalitional rationality is introduced by embracing the conditions of individual and collective rationality with some combination of the concepts of Nash and Berge equilibria. Sufficient conditions are established under which the game has a coalitional equilibrium of this type. In addition, the existence of such a solution in mixed strategies is proved in the case of continuous payoff functions and compact strategy sets of players.
About the authors
V. I Zhukovskiy
Moscow State University
Author for correspondence.
Email: zhkvlad@yandex.ru
Moscow, Russia
L. V Zhukovskaya
Central Economics and Mathematics Institute, Russian Academy of Sciences
Email: zhukovskaylv@mail.ru
Moscow, Russia
L. V Smirnova
State University of Humanities and Technology
Email: smirnovalidiya@rambler.ru
Orekhovo-Zuyevo, Russia
M. I Vysokos
State University of Humanities and Technology
Email: mvysokos@mail.ru
Orekhovo-Zuyevo, Russia
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