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<p>We propose an optimization-based framework to define solutions for stochastic cooperative games. We construct excess-based preference functions that evaluate coalitional (or individual) dissatisfaction through the expected square and variance of excesses, with a parameter capturing risk aversion, neutrality and loving. Aggregating players’ preferences yields tractable optimization models, and solutions are defined as their minimizers under efficiency. We study two allocation paradigms: a decomposition rule that separates expected worth and residual uncertainty, and a cohesive proportional rule that distributes total random worth proportionally. For both paradigms, we derive optimal allocations, provide existence (uniqueness) conditions, and explain how risk attitudes shape risk sharing. Simple examples illustrate how the function measures risk attitudes and supports decision making in stochastic cooperative settings.</p>

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Solutions of Stochastic Cooperative Games with Excess-Based Preferences Through Optimization Method

  • 期刊论文

  • 发表日期：

    2026年6月20日

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  • Pan-Fei Sun,
  • Yi-Chen Yang,
  • Gen-Jiu Xu,
  • Guang-Jing Yang

摘要

We propose an optimization-based framework to define solutions for stochastic cooperative games. We construct excess-based preference functions that evaluate coalitional (or individual) dissatisfaction through the expected square and variance of excesses, with a parameter capturing risk aversion, neutrality and loving. Aggregating players’ preferences yields tractable optimization models, and solutions are defined as their minimizers under efficiency. We study two allocation paradigms: a decomposition rule that separates expected worth and residual uncertainty, and a cohesive proportional rule that distributes total random worth proportionally. For both paradigms, we derive optimal allocations, provide existence (uniqueness) conditions, and explain how risk attitudes shape risk sharing. Simple examples illustrate how the function measures risk attitudes and supports decision making in stochastic cooperative settings.