Abstract: In some cases, the optimal solution is not unique. Because the player’s payoff in each optimal solution is different, each player would pursue the optimal solution which can maximize his own payoff to the extent. To resolve this problem, we proposed a bargainging model of the cooperative assignment problem and a compensation function in the perspective of individual rationality. With the bargaining model and the compensation function, we proposed a mehtod to ensure the uniqueness of the assignment problem's optimal solution.

Key words: the assignment problem, game theory, individual rationality, Nash equilibrium, bargaining solution