Convergence of probabilistic automatic negotiation: mutual maximum likelihood estimation

This study deals with a bilateral automatic negotiation system composed of two players. One player proposes offers to the other one mutually based on its own utility and strategy and the estimation of the same of the opponent. The estimation is based on the history of the offers made by the opponent player. Therefore, the total system has a feedback structure between two players, and the agreement of the negotiation is regarded as a convergence to their equilibrium states. Furthermore, we suppose that the offers are generated probabilistically based on the utility, and the maximum likelihood estimation is used for the opponent estimation. The resultant system is called a mutual maximum likelihood estimation system. To analyze the condition for the agreement, we examine the convergence of the mutual maximum likelihood estimation system under appropriate conditions, and show that the estimated parameters converge to their true values.