广义合作博弈的斯卡夫定理
On Scarf's theorem for Generalized Cooperative Games
AI总结：
本文研究非转移效用合作博弈的推广模型，引入核心与分数核心概念，证明分数核心非空等价于相关覆盖同伦非平凡，进而得到广义合作博弈的斯卡夫型定理。
摘要：
本文研究非转移效用合作博弈的一种推广形式。在我们的模型中，联盟被企业取代：每家企业被分配一个资源向量，而联盟的效用向量集被替换为该企业在共同支付空间中的可行支付向量的一般综合集。我们为这类博弈引入核心和分数核心的概念，并将它们的存在性与博弈相关联的覆盖的同伦不变量联系起来。主要结果表明，当且仅当相关覆盖在同伦意义下非平凡时，分数核心非空。由此，我们得到了广义合作博弈的斯卡夫型定理。
英文摘要：
In this paper, we study a generalization of cooperative games with non-transferable utility. Our model is motivated by Shapley's proof of Scarf's theorem, which revealed a deep connection between KKM-type theorems and cooperative games. In recent decades, further developments have established deeper connections between algebraic topology and combinatorial KKM-type fixed-point theorems. We explore the consequences of these developments for cooperative game theory. In our model, coalitions are replaced by firms, each represented by a resource vector and a set of feasible payoff vectors in a common payoff space. We define the core and fractional core for these games and relate their nonemptiness to homotopy invariants of covers associated with the game. Consequently, we obtain a Scarf-type theorem for generalized cooperative games. This framework allows us to model cooperative games with threats and political games.
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。
