Individuals make interactions and exchanges behind a market which provides them with information and makes them take their separate decisions, coordinate and form coalitions and agreements that give them more power and advantages to maximize the benefits. In this paper, I will consider assignment markets where buyers and sellers play a double role as buyers and sellers and exchange two products separately and worth a benefit at the end of the game. I will study the core, the competitive equilibrium, and I will introduce market value, which I named the bargaining and collaboration value.