Abstract: The game-theoretic solutions defined in two-sided market allow the interests of agents on the same side of the market to be simultaneously maximized. The theoretic basis of such kind of optimization is the stability of the selection matching. This paper uses game-theoretic method to study the optimization in many-to-one two-sided matching market. Under the presence of substitutable and LAD(Law of Aggregate Demand) preferences, we prove that the selections made by firms produce a stable matching, so do the selections made by workers.

Key words: matching game, stable matching, substitutable preference