On Coalitional Rationality in a Three-Person Game
- 作者: Zhukovskiy V.I1, Zhukovskaya L.V2, Smirnova L.V3, Vysokos M.I3
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隶属关系:
- Moscow State University
- Central Economics and Mathematics Institute, Russian Academy of Sciences
- State University of Humanities and Technology
- 期: 编号 1 (2025)
- 页面: 40-45
- 栏目: Control in Social and Economic Systems
- URL: https://journal-vniispk.ru/1819-3161/article/view/351156
- ID: 351156
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详细
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.
作者简介
V. Zhukovskiy
Moscow State University
编辑信件的主要联系方式.
Email: zhkvlad@yandex.ru
Moscow, Russia
L. Zhukovskaya
Central Economics and Mathematics Institute, Russian Academy of Sciences
Email: zhukovskaylv@mail.ru
Moscow, Russia
L. Smirnova
State University of Humanities and Technology
Email: smirnovalidiya@rambler.ru
Orekhovo-Zuyevo, Russia
M. Vysokos
State University of Humanities and Technology
Email: mvysokos@mail.ru
Orekhovo-Zuyevo, Russia
参考
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