An novel ADM for finding Cournot equilibria of bargaining problem with alternating offers

Bargaining is a basic game in economic practice. Cournot duopoly game is an important model in bargaining theory and is well studied in the literatures. Recently, asymmetry information [20] and incomplete information [19], limited individual rationality [2] and slightly altruistic equilibrium [10] are introduced into bargaining theory. And computational game theory also comes into being a new hot-research field. In this paper, we propose a novel method to compute Cournot equilibria of bargaining problem with alternating offers. The method is Inexact Proximal Alternating Directions Method. In the proposed method, the idea of alternating directions method corresponds to alternating offers, and the inexact term corresponds to asymmetry information and limited individual rationality in practice. Under some suitable conditions, we prove convergence of the proposed method (i.e., the strategic sequence generated by the proposed method converges to the Cournot equilibria of this game). Numerical tests show rationality, efficiency and applicability of the proposed method.