Game theoretic models of matching and product differentiation.

摘要

My dissertation consists of two essays on markets. Game theory is the common denominator for my analysis of a labor market for American physicians and a market for differentiated products.; In two sided matching markets, Roth and Peranson (1999) observe that the number of agents who receive different mates at different stable matchings remains small as the market grows, so long as agents' preferences do not grow in length. The present paper explores and extends this result both theoretically and computationally. We prove that the number of stable matchings is finite even in infinitely large markets as long as preference length is finite and provide analytical upper bounds to the number of agents being matched differently under different stable matchings. When preferences agents have are sufficiently short these upper bounds imply that the number of stable matchings is small and independent of the size of the market.; Chapter 2 discusses horizontal product differentiation in multidimensional product space by more than two firms. Irmen and Thisse (1998) show that two firms competing with multi-characteristic products differentiate them in characteristic completely, while keeping them identical in all the others. I show that their min-...-min-max differentiation result is not robust with respect to number of firms. We give a characterization of local equilibria for markets with two, three, and four firms that can differentiate their products in two dimensions. The symmetric equilibrium with three firms implies that none of these firms are completely differentiated in any dimension. Furthermore, the degree of equilibrium differentiation is smaller with four firms than with three firms. First step toward generalization of the properties of equilibria where there are k firms competing in n dimensional product market is presented.