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A method of computing equilibrium for the partnership formation

In the model of partnership formation, every agent is in hot pursuit of maximizing his own utility. Doft Talman and Zaifu Yang have revealed the necessary condition of the existence of partnership equilibrium, however, the methods of how to compute the equilibrium are not given. The paper presents a method to compute the partnership utility equilibrium based on socially optimal assignment. Firstly, the partnership groups with social optimality are exhausted in the all possible cooperative pairs, and then under the condition of the existence of equilibrium, an algorithm is given to get the Equilibrium Utility Vector so as to approach the equilibrium status after multiple iterations. This solution to computing partnership payoff equilibrium can be obtained in O(n2) time. At last, to verify the method given by this paper, an example of municipal water supply planning is given to illustrate the correctness and effectiveness.