Bargaining is a basic game in economic practice. Cournot duopoly game is an important model in bargaining theory. Recently, asymmetry information  and incomplete information , limited individual rationality  and slightly altruistic equilibrium  are introduced into bargaining theory. And computational game theory come into being a new research field. In this paper, we propose a novel method to compute Cournot point of duopoly model with alternating o®ers, this method is Inexact Proximal Alternating Directions Method. In the proposed method, the idea of alternating directions method corresponds to alternating offers, and inexact proximal point term corresponds to asymmetry information and limited individual rationality in practice. Under suitable conditions, we prove convergence of the proposed method. Numerical experimentation show its rationality, e±ciency and applicability of the proposed method.