Multi-person cooperative games: The nucleoli approach and assignment games.

摘要

Existence and uniqueness have been major concerns for many solution concepts in multi-person cooperative game theory. The nucleolus, however, is among those which do not exist and is unique for each partition structure in any game. It has been investigated throughout the literature, particularly with respect to the grand coalition where the nucleolus provides a unique outcome. Yet surprisingly little has been written about the nucleoli for possible partition structures other than the grand coalition.;In this dissertation, the nucleoli for possible partition structures in all three-person games (as well as other classes of multi-person cooperative games) are investigated. A proof is given which demonstrates that, whenever the core is the empty set, the nucleolus for the grand coalition is dominated by the nucleoli for other partition structures. Also introduced is a new solution concept--itself a modification of the classical nucleolus--which enforces full cooperation among participants. Algebraic formulas to compute the nucleoli and the modified nucleolus are then presented.;In the second part of this dissertation, properties of the core, the bargaining simplex, and the nucleolus for the Shapley-Shubik assignment games are investigated. The bargaining simplex for such games is a line segment which is expressed in terms of a real parameter. For those assignment games where the core contains the bargaining simplex, the nucleolus for the grand coalition is the midpoint of the bargaining simplex. The idea of the bargaining simplex extends to include the class of multisided assignment games where there are m sets of players, each of different types.;Several algorithms already exist for computing the nucleolus of games in general, as well as for the Shapley-Shubik assignment games in particular, e.g., by Solymosi and Raghavan (1994). The approach presented in this dissertation circumvent the otherwise use of linear programming (and/or balanced sets) frequently employed by these algorithms.