Abstract
Two-sided matching is a popular issue in game theory. Several kinds of two-sided matching have been analyzed and modeled as games [1]. Shapley and Shubik [2] investigate a kind of two-sided matching called a two-sided market, and model it as a coalitional game called the assignment game. It is shown in [2][3] that some elements of the core of the assignment game can be obtained by solving a linear programming problem. Nonetheless, not all elements of the core of the assignment game are given. In this thesis, we consider a variant of the two-sided market and model it as a coalitional game called a horse trading game. In this game, the goods are homogeneous horses, i.e., everyone in this game values any two horses at the same price. Moreover, there are only one owner and multiple nonowners in this game. The owner has multiple horses and each nonowner has no horse. In addition, we assume that every nonowner buys at most one horse in this game, and that everyone's valuation of a horse is different from each other in this game. The main contribution in this thesis is that we give an explicit expression of the core of the horse trading game.