Near-optimal no-regret algorithms for zero-sum games

Games and Economic Behavior

Volumn 92, Issue , 2015, Pages 327-348

  Daskalakis, Constantinos ^a   Deckelbaum, Alan ^b   Kim, Anthony ^c  

^a Department of Electrical Engineering and Computer Science   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c Stanford University   (United States)

Author keywords

Learning; No regret dynamics; Repeated games; Zero sum games

Indexed keywords

EID: 84938960088     PISSN: 08998256     EISSN: 10902473     Source Type: Journal    
DOI: 10.1016/j.geb.2014.01.003     Document Type: Article

References (26)

1. Adler I. The equivalence of linear programs and zero-sum games. Int. J. Game Theory 2013, 42(1):165-177.
2. Babichenko Y. Completely Uncoupled Dynamics and Nash Equilibria. Discussion Pap. Ser 2010, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem.
3. Blum A., Mansour Y. From external to internal regret. J. Mach. Learn. Res. 2007, 8:1307-1324.
4. Brandt F., Fischer F., Harrenstein P. On the rate of convergence of fictitious play. Proceedings of the 3rd International Symposium on Algorithmic Game Theory (SAGT) 2010, 102-113.
5. Brown G.W. Iterative solution of games by fictitious play. Act. Anal. Product. Alloc. 1951, 13(1):374-376.
6. Cesa-Bianchi N., Lugosi G. Prediction, Learning, and Games 2006, Cambridge University Press.
7. Foster D.P., Vohra R. Calibrated learning and correlated equilibrium. Biometrika 1998, 85:379-390.
8. Foster D., Young H.P. Regret testing: learning to play Nash equilibrium without knowing you have an opponent. Theoretical Econ. 2006, 1:341-367.
9. Freund Y., Schapire R. Adaptive game playing using multiplicative weights. Games Econ. Behav. 1999, 29:79-103.
10. Gilpin A., Hoda S., Peña J., Sandholm T. Gradient-based algorithms for finding Nash equilibria in extensive form games. Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE) 2007, 57-69.
11. Gilpin A., Hoda S., Peña J., Sandholm T. Smoothing techniques for computing Nash equilibria of sequential games. Math. Operations Res. 2010, 35(2):494-512.
12. Gilpin A., Peña J., Sandholm T. First-order algorithm with O(ln(1/ε)) convergence for ε-equilibrium in two-person zero-sum games. Proceedings of the 23rd Conference on Artificial Intelligence (AAAI) 2008, 75-82.
13. Harris C. On the rate of convergence of continuous-time fictitious play. Games Econ. Behav. 1998, 22:238-259.
14. Hart S., Mas-Colell A. A simple adaptive procedure leading to correlated equilibrium. Econometrica 2000, 68(5):1127-1150.
15. Hart S., Mas-Colell A. Uncoupled dynamics do not lead to Nash equilibrium. Amer. Econ. Rev. 2003, 93:1830-1836.
16. Karmarkar N. A new polynomial-time algorithm for linear programming. Proceedings of the 16th Annual ACM Symposium on Theory of Computing (STOC) 1984, 302-311.
17. Khachiyan L.G. A polynomial algorithm in linear programming. Soviet Math. Dokl. 1979, 20(1):191-194.
18. Littlestone N., Warmuth M. The weighted majority algorithm. Inf. Comput. 1994, 108:212-261.
19. Myerson R.B. Nash equilibrium and the history of economic theory. J. Econ. Lit. 1999, 37:1067-1082.
20. Nash J. Noncooperative games. Ann. of Math. 1951, 54:289-295.
21. Nesterov Y. Excessive gap technique in nonsmooth convex minimization. SIAM J. Optim. 2005, 16(1):235-249.
22. Nesterov Y. Smooth minimization of non-smooth functions. Math. Program. 2005, 103(1):127-152.
23. von Neumann J. Zur Theorie der Gesellschaftsspiele. Math. Ann. 1928, 100:295-320.
24. von Neumann J., Morgenstern O. Theory of Games and Economic Behavior 1944, Princeton University Press.
25. Robinson J. An iterative method of solving a game. Ann. of Math. 1951, 54:296-301.
26. Zinkevich M. Online convex programming and generalized infinitesimal gradient ascent. Proceedings of the 20th International Conference on Machine Learning (ICML) 2003, 928-936.