An Alternating Direction Method for Nash Equilibrium of Two-Person Games with Alternating Offers

In this paper, we propose a method for finding a Nash equilibrium of two-person games with alternating offers. The proposed method is referred to as the inexact proximal alternating direction method. In this method, the idea of alternating direction method simulates alternating offers in the game, while the inexact solutions of subproblems can be matched to the assumptions of incomplete information and bounded individual rationality in practice. The convergence of the proposed method is proved under some suitable conditions. Numerical tests show that the proposed method is competitive to the state-of-the-art algorithms.