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.
KeywordsComputational game theory Nash equilibrium Inexact proximal point method Alternating direction method
This work was supported by the Natural Science Foundation of China (61170308), the Natural Science Foundation of FuJian Province (2011J01008), and FuJian Province Education Department (JA11033). The authors are very grateful to the editor and two anonymous referees for their constructive comments which helped improving the quality of the manuscript greatly.
- 1.von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior (sixtieth Anniversary edition). Princeton University Press, Princeton (2004) Google Scholar
- 3.McKelvey, R.D., McLennan, A.: Computation of equilibria in finite games. In: Amman, H., Kendrick, D., Rust, J. (eds.) Handbook of Computational Economics, vol. 1, pp. 87–142. Elsevier, Amsterdam (2000) Google Scholar
- 4.von Stengel, B.: Computing equilibria for two-person games. In: Aumann, R., Hart, S. (eds.) Handbook of Game Theory, vol. 3, pp. 1723–1759. North-Holland, Amsterdam (2002) Google Scholar
- 7.Yuan, Y.X.: A trust region algorithm for Nash equilibrium problems. Pac. J. Optim. 7(1), 125–138 (2010) Google Scholar
- 11.Xu, L.L., Han, D.R.: A proximal alternating direction method for weakly coupled variational inequalities. Pac. J. Optim. (2012, to appear) Google Scholar