Solving two-person zero-sum repeated games of incomplete information

Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

Volumn 2, Issue , 2008, Pages 885-892

  Gilpin, Andrew ^a   Sandholm, Tuomas ^a  

^a Computer Science Department Carnegie Mellon University ^*  (United States)

Author keywords

Computational game theory; Equilibrium finding; Non convex optimization; Two person zero sum incomplete information repeated games

Indexed keywords

ALGORITHMS; AUTONOMOUS AGENTS; CONVEX OPTIMIZATION; MULTI AGENT SYSTEMS; OPTIMAL SYSTEMS;

ALGORITHM FOR SOLVING; ARBITRARY ACCURACY; COMPUTATIONAL GAME THEORIES; INCOMPLETE INFORMATION; NONCONVEX OPTIMIZATION; OPTIMAL STRATEGIES; OPTIMIZATION PROBLEMS; REPEATED GAMES;

COMPUTER GAMES;

EID: 84899991152     PISSN: 15488403     EISSN: 15582914     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (26)

1. R. J. Aumann and M. Maschler. Repeated Games with Incomplete Information. MIT Press, 1995.
2. With the collaboration of R. Stearns. This book contains updated versions of four papers originally appearing in Report of the U.S. Arms Control and Disarmament Agency, 1966-68.
3. D. Blackwell. An analog of the minmax theorem for vector payoffs. Pacific Journal of Mathematics, 6:1-8, 1956.
4. R. Brafman and M. Tennenholtz. A near-optimal polynomial time algorithm for learning in certain classes of stochastic games. Artificial Intelligence, 121:31-47, 2000.
5. C. Carathéodory. Uber den Variabiletätsbereich der Fourier'schen Konstanten von positiven harmonischen Funktionen. Rendiconti del Circolo Matematico de Palermo, 32:193-217, 1911.
6. V. Chvátal. Linear Programming. W. H. Freeman and Company, New York, NY, 1983.
7. B. De Meyer. Repeated games, duality and the central limit theorem. Mathematics of Operations Research, 21:237-251, 1996.
8. B. De Meyer and D. Rosenberg. "Cav u" and the dual game. Mathematics of Operations Research, 24:619-626, 1999.
9. D. Fudenberg and D. Levine. The Theory of Learning m Games. MIT Press, 1998.
10. M. Garey and D. Johnson. Computers and Intractability. W. H. Freeman and Company, 1979.
11. S. Hart. Nonzero-sum two-person repeated games with incomplete information. Mathematics of Operations Research, 10:117-153, 1985.
12. J. Hu and M. P. Wellman. Nash Q-learning for general-sum stochastic games. Journal of Machine Learning Research, 4:1039-1069, 2003.
13. L. Khachiyan. A polynomial algorithm in linear programming. Soviet Math. Doklady, 20:191-194, 1979.
14. M. Littman. Markov games as a framework for multi-agent reinforcement learning. In Int. Conf. on Machine Learning (ICML), pages 157-163, 1994.
15. M. Littman and P. Stone. A polynomial-time Nash equilibrium algorithm for repeated games. In Proc. of the ACM Conference on Electronic Commerce (ACM-EC), pages 48-54, San Diego, CA, 2003.
16. J.-F. Mertens and S. Zamir. The value of two-person zero-sum repeated games with lack of information on both sides. International Journal of Game Theory, 1:39-64, 1971.
17. R. Myerson. Game Theory: Analysis of Conflict. Harvard University Press, Cambridge, 1991.
18. Y. Nesterov. Introductory Lectures on Convex Optimization: A Basic Course. Kluwer Academic Publishers, 2004.
19. J.-P. Ponssard and S. Sorin. The L-P formulation of finite zero-sum games with incomplete information. International Journal of Game Theory, 9:99-105.
20. R. T. Rockafellar. Convex Analysis. Princeton University Press, 1970.
21. T. Sandholm. Perspectives on multiagent learning. Artificial Intelligence, 171:382-391, 2007.
22. L. S. Shapley. Stochastic games. Proceedings of the National Academy of Sciences, 39:1095-1100, 1953.
23. S. Sorin. A First Course on Zero-Sum Repeated Games. Springer, 2002.
24. J. von Neumann. Zur Theorie der Gesellschaftsspiele. Mathematische Annalen, 100:295-320, 1928.
25. S. J. Wright. Primal-Dual Interior-Point Methods. SIAM, Philadelphia, PA, 1997.
26. S. Zamir. Repeated games of incomplete information: Zero-sum. In R. J. Aumann and S. Hart, editors, Handbook of Game Theory, Vol. I, pages 109-154. North Holland, 1992.