Topics on Game Theory

First, we will discuss the several elements that characterize a two-sided matching market and the concept of setwise-stability versus core. Then,we will model several of these markets (one-to-one, many-to-one and many-to-many, in the discrete and continuous cases) under the game-theoretic approach and will define for all of them the stability concept, establishing its relationship with the core and the competitive equilibrium concepts. Afterwards, we will introduce the theory of stable matching model by focusing on both the cooperative and non-cooperative aspects of the one-to-one matching markets.