Fuzzy Coalitions and Solutions of Cooperative Games: Beyond the Market Solutions

在传统的市场游戏中，联盟收益是根据玩家向他们参与的联盟贡献每一笔初始捐赠的协议来分配给每个玩家的。相反，在模糊市场博弈中，参与者不一定要向联盟贡献所有初始捐赠，他们可以通过向联盟贡献部分初始捐赠来自由决定他们的承诺程度。众所周知，在具有同质可分商品的经济体中，模糊核心分配与竞争均衡分配重合。如果没有模糊联盟，一般情况下，就会有无法通过市场机制实现的核心配置。然而，在这项研究中，我证明了模糊核心分配可以通过市场机制实现。

In traditional market games, coalitional payoffs are allocated to each player contingent upon the agreement that players contribute every initial endowment to the coalitions they are participating. On the contrary, in fuzzy market games, players do not necessarily have to contribute every initial endowment to the coalitions and they are free to decide their degree of commitment by contributing partially their initial endowment to the coalitions. It is well known in the literature that in economies with homogeneous divisible commodities fuzzy core allocations coincide with competitive equilibrium allocations. Without fuzzy coalitions, in general there is a core allocation that cannot be realized through the market mechanism. Nevertheless, in this research, I demonstrated that fuzzy core allocations can be attained by the market mechanism.