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<p>We introduce a&#xa0;concept of coalition equilibrium in the paper. On the synthesis basis of the concepts of individual and collective rationality (from theory of cooperative games without side payments) and the definition of coalition rationality proposed in the present investigation, we formalize a&#xa0;coalition equilibrium strategy profile in a&#xa0;conflict of three persons under uncertainty. We establish sufficient conditions for the existence of the coalition equilibrium strategy profile, which are reduced to the construction of a&#xa0;saddle point of the special Germeier convolution of the guarantees of the payoff function. Finally, following the approach of Emile Borel and John Nash, we prove existence of the coalition equilibrium strategy profile in mixed strategies under “habitual” restrictions for mathematical programming (compactness of sets of player strategies and continuity of payoff functions).</p>

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The Coalition Rationality in Mixed Strategies

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Vladislav I. Zhukovskiy,
  • Lidiya V. Zhukovskaya,
  • Konstantin N. Kudryavtsev,
  • Lidiya V. Smirnova

摘要

We introduce a concept of coalition equilibrium in the paper. On the synthesis basis of the concepts of individual and collective rationality (from theory of cooperative games without side payments) and the definition of coalition rationality proposed in the present investigation, we formalize a coalition equilibrium strategy profile in a conflict of three persons under uncertainty. We establish sufficient conditions for the existence of the coalition equilibrium strategy profile, which are reduced to the construction of a saddle point of the special Germeier convolution of the guarantees of the payoff function. Finally, following the approach of Emile Borel and John Nash, we prove existence of the coalition equilibrium strategy profile in mixed strategies under “habitual” restrictions for mathematical programming (compactness of sets of player strategies and continuity of payoff functions).