圆锥规划中的合作及其在控制、生产和投资组合中的应用
Cooperation in Conic Programming with Applications to Control, Production, and Portfolio
AI总结：
介绍合作圆锥博弈类，统一多种基于优化的合作博弈。利用圆锥规划和对偶理论推导核心收益分配条件及计算方法，通过多应用展现框架表达力。
摘要：
我们引入合作圆锥博弈类，这是一类新的可转移效用博弈，其特征函数可通过求解圆锥优化问题计算。该框架统一多种基于优化的合作博弈，利用圆锥规划性质和对偶理论推导核心收益分配条件及计算方法，通过应用展示其表达力。
英文摘要：
We introduce the class of cooperative conic games, a new family of transferable utility games whose characteristic function can be computed by solving a conic optimization problem. This framework unifies a broad range of optimization-based cooperative games within a common mathematical formulation, encompassing linear, second-order cone, semidefinite, and other convex nonlinear optimization problems admitting conic representations. Exploiting the structural properties of conic programs and conic duality theory, we derive general conditions ensuring the existence of core payoff allocations (or cost shares) and show how such allocations can be computed directly from optimal dual solutions. In particular, the proposed methodology replaces combinatorial verification procedures for core nonemptiness with tractable optimization-based criteria. The expressive power of the framework is illustrated through several representative applications. We show that it models cooperation in multi-agent optimal control, generalizes linear production games to nonlinear production settings such as Cobb--Douglas models, introduces cooperative formulations for portfolio selection under Markowitz, conditional value-at-risk, and entropic risk measures, and unifies a broad class of combinatorial optimization games through exact conic reformulations. These examples involve the most relevant cones in modern convex optimization, highlighting both the versatility of the proposed framework and its potential to strengthen the interaction between mathematical programming and cooperative game theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
