Coalitional Games with Transferable Utility
摘要
In this chapter, we will study (coalitional) games with transferable utility, also called TU games. In these games, a set of individuals will share a certain amount of value (e.g., the cost or the benefit of a project) among themselves cooperatively. Each subset of these individuals is called a coalition. The utility of each coalition is exogenously given, and the utility is transferable in the sense that each coalition can freely divide among its members the total value that this coalition can secure as a whole. In Sect. 14.1, we will provide general definitions and, in Sect. 14.2, we will define for coalitional games a solution concept, called the core, which is the set of utility allocations that ensures that no coalition of individuals has an incentive to leave their coalitions to form, or join into, another coalition. We will motivate this concept with several examples and also present a necessary and sufficient condition under which the core is nonempty. Next, in Sect. 14.3, we will present another solution concept, called the Shapley value. According to this concept, the value of each individual in the coalitional game will be equal to her average marginal contribution over all possible orderings in which the individuals in the game may join the largest coalition.