The state of solving large incomplete-information games, and application to poker

AI Magazine

Volumn 31, Issue 4, 2010, Pages 13-32

  Sandholm, Tuomas ^a  

^a Carnegie Mellon University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GAME THEORY;

ABSTRACTION ALGORITHMS; ACTION SELECTION; FINDING ALGORITHM; INCOMPLETE INFORMATION GAMES; INFORMATION HIDING; NASH EQUILIBRIA; SAFETY GUARANTEES; SOLUTION QUALITY;

ABSTRACTING;

EID: 79959727828     PISSN: 07384602     EISSN: None     Source Type: Journal    
DOI: 10.1609/aimag.v31i4.2311     Document Type: Article

References (59)

1. Abbott, T.; Kane, D.; and Valiant, P. 2005. On the Complexity of Two-Player Win-Lose Games. In Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS-05). Los Alamitos, CA: IEEE Computer Society.
2. Ankenman, J., and Chen, B. 2006. The Mathematics of Poker. Pittsburgh, PA: ConJelCo LLC.
3. Bard, N., and Bowling, M. 2007. Particle Filtering for Dynamic Agent Modelling in Simplified Poker. In Proceedings of the 22nd AAAI Conference on Artificial Intelligence (AAAI-07), 515-521. Menlo Park, CA: AAAI Press. (Pubitemid 350149622)
4. Billings, D.; Burch, N.; Davidson, A.; Holte, R.; Schaeffer, J.; Schauenberg, T.; and Szafron, D. 2003. Approximating Game-Theoretic Optimal Strategies for Full-scale Poker. In Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI-03). San Francisco: Morgan Kaufmann Publishers.
5. Billings, D.; Davidson, A.; Schaeffer, J.; and Szafron, D. 2002. The Challenge of Poker. Artificial Intelligence 134(1- 2): 201-240. (Pubitemid 34086584)
6. Billings, D.; Papp, D.; Schaeffer, J.; and Szafron, D. 1998. Opponent Modeling in Poker. In Proceedings of the 15th National Conference on Artificial Intelligence (AAAI-98), 493-499. Menlo Park, CA: AAAI Press.
7. Blum, B.; Shelton, C. R.; and Koller, D. 2006. A Continuation Method for Nash Equilibria in Structured Games. Journal of Artificial Intelligence Research 25: 457-502. (Pubitemid 43800053)
8. Chen, X., and Deng, X. 2006. Settling the Complexity of 2-Player Nash Equilibrium. In Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS). Los Alamitos, CA: IEEE Computer Society.
9. Ciancarini, P., and Favini, G. P. 2009. Monte Carlo Tree Search Techniques in the Game of Kriegspiel. In Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI-09). Menlo Park, CA: AAAI Press.
10. Conitzer, V., and Sandholm, T. 2006. Computing the Optimal Strategy to Commit to. In Proceedings of the 11th ACM Conference on Electronic Commerce, 83-92. New York: Association for Computing Machinery.
11. Daskalakis, C.; Goldberg, P.; and Papadimitriou, C. 2008. The Complexity of Computing a Nash Equilibrium. SIAM Journal on Computing 39(1): 195-259
12. Etessami, K., and Yannakakis, M. 2007. On the Complexity of Nash Equilibria and Other Fixed Points (Extended Abstract). In Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS-07), 113-123. Los Alamitos, CA: IEEE Computer Society.
13. Ganzfried, S., and Sandholm, T. 2010. Computing Equilibria by Incorporating Qualitative Models. In Proceedings of the Ninth International Conference on Autonomous Agents and MultiAgent Systems (AAMAS 2009). Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
14. Ganzfried, S., and Sandholm, T. 2009. Computing Equilibria in Multiplayer Stochastic Games of Imperfect Information. In Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI-09). Menlo Park, CA: AAAI Press.
15. Ganzfried, S., and Sandholm, T. 2008. Computing an Approximate Jam/Fold Equilibrium for 3-Agent No-Limit Texas Hold'em Tournaments. In Proceedings of the 8th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS). Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
16. Gilpin, A., and Sandholm, T. 2010. Speeding Up Gradient- Based Algorithms for Sequential Games. In Proceedings of the Ninth International Conference on Autonomous Agents and MultiAgent Systems (AAMAS 2010). Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
17. Gilpin, A., and Sandholm, T. 2008a. Expectation-Based Versus Potential-Aware Automated Abstraction in Imperfect Information Games: An Experimental Comparison Using Poker. In Proceedings of the 23rd AAAI Conference on Artificial Intelligence (AAAI-08). Short paper. Menlo Park, CA: AAAI Press.
18. Gilpin, A., and Sandholm, T. 2008b. Solving Two-Person Zero-Sum Repeated Games of Incomplete Information. In Proceedings of the Seventh International Conference on Autonomous Agents and MultiAgent Systems (AAMAS 2008). Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
19. Gilpin, A., and Sandholm, T. 2007a. Better Automated Abstraction Techniques for Imperfect Information Games, with Application to Texas Hold'em Poker. In Proceedings of the 6th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS 2007), 1168-1175.Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
20. Gilpin, A., and Sandholm, T. 2007b. Lossless Abstraction of Imperfect Information Games. Journal of the ACM 54(5): 1-32.
21. Gilpin, A., and Sandholm, T. 2006. A Competitive Texas Hold'em Poker Player via Automated Abstraction and Real-Time Equilibrium Computation. In Proceedings of the 21st National Conference on Artificial Intelligence (AAAI-06), 1007-1013. Menlo Park, CA: AAAI Press. (Pubitemid 44711495)
22. Gilpin, A.; Hoda, S.; Pena, J.; and Sandholm, T. 2007. Gradient-Based Algorithms for Finding Nash Equilibria in Extensive Form Games. In Proceedings of the 3rd International Workshop on Internet and Network Economics (WINE '07). Berlin: Springer-Verlag.
23. Gilpin, A.; Pena, J.; and Sandholm, T. 2008. First-Order Algorithm with O(log(1/ε)) Convergence for e-Equilibrium in Games. In Proceedings of the 23rd AAAI Conference on Artificial Intelligence (AAAI-08). Menlo Park, CA: AAAI Press.
24. Gilpin, A.; Sandholm, T.; and Sorensen, T. B. 2008. A Heads-Up No-Limit Texas Hold'em Poker Player: Discretized Betting Models and Automatically Generated Equilibrium-Finding Programs. In Proceedings of the Seventh International Conference on Autonomous Agents and MultiAgent Systems (AAMAS 2008). Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
25. Gilpin, A.; Sandholm, T.; and Sorensen, T. B. 2007. Potential- Aware Automated Abstraction of Sequential Games, and Holistic Equilibrium Analysis of Texas Hold'em Poker. In Proceedings of the 22nd AAAI Conference on Artificial Intelligence (AAAI-07). Menlo Park, CA: AAAI Press.
26. Goffin, J.-L. 1977. On the Convergence Rate of Subgradient Optimization Methods. Mathematical Programming 13(1): 329-347.
27. Govindan, S., and Wilson, R. 2003. A Global Newton Method to Compute Nash Equilibria. Journal of Economic Theory 110(1): 65-86. (Pubitemid 36802525)
28. Hoda, S.; Gilpin, A.; Pena, J.; and Sandholm, T. 2010. Smoothing Techniques for Computing Nash Equilibria of Sequential Games. Mathematics of Operations Research 35(2): 494-512.
29. Jain, M.; Tsai, J.; Pita, J.; Kiekintveld, C.; Rathi, S.; Ordóñez, F.; and Tambe, M. 2010. Software Assistants for Randomized Patrol Planning for The LAX Airport Police and The Federal Air Marshals Service. Interfaces 40(4): 267-290.
30. Johanson, M., and Bowling, M. 2009. Data Biased Robust Counter Strategies. Paper presented at the 12th International Conference on Artificial Intelligence and Statistics (AISTATS), Clearwater Beach, FL. 16-18 April.
31. Johanson, M.; Zinkevich, M.; and Bowling, M. 2007. Computing Robust Counter-Strategies. In Proceedings of the 21st Annual Conference on Neural Information Processing Systems (NIPS 2007). Cambridge, MA: The MIT Press.
32. Kiekintveld, C.; Tambe, M.; and Marecki, J. 2010. Robust Bayesian Methods for Stackelberg Security Games (Extended Abstract). In Proceedings of the Ninth International Conference on Autonomous Agents and MultiAgent Systems (AAMAS 2010). Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
33. Koller, D., and Pfeffer, A. 1997. Representations and Solutions for Game-Theoretic Problems. Artificial Intelligence 94(1): 167-215. (Pubitemid 127371450)
34. Koller, D.; Megiddo, N.; and von Stengel, B. 1996. Efficient Computation of Equilibria for Extensive Two-Person Games. Games and Economic Behavior 14(2): 247-259. (Pubitemid 126169181)
35. Kuhn, H. W. 1950. A Simplified Two-Person Poker. In Contributions to the Theory of Games, Annals of Mathematics Studies 24, ed. H. W. Kuhn and A. W. Tucker, volume 1, 97-103. Princeton, NJ: Princeton University Press.
36. Lanctot, M.; Waugh, K.; Zinkevich, M.; and Bowling, M. 2009. Monte Carlo Sampling for Regret Minimization in Extensive Games. In Proceedings of the 23rd Annual Conference on Neural Information Processing Systems (NIPS 2009), 1078-1086. Cambridge, MA: The MIT Press.
37. Letchford, J., and Conitzer, V. 2010. Computing Optimal Strategies to Commit to in Extensive-Form Games. In Proceedings of the 11th ACM Conference on Electronic Commerce, 83-92. New York: Association for Computing Machinery.
38. Milgrom, P., and Roberts, J. 1996. Coalition-Proofness and Correlation with Arbitrary Communication Possibilities. Games and Economic Behavior 17(1): 113-128. (Pubitemid 126164735)
39. Miltersen, P. B., and Sorensen, T. B. 2010. Computing a Quasi-Perfect Equilibrium of a Two-Player Game. Economic Theory 42(1): 175-192.
40. Miltersen, P. B., and Sorensen, T. B. 2008. Fast Algorithms for Finding Proper Strategies in Game Trees. In Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 874-883. Philadelphia, PA: Society for Industrial and Applied Mathematics.
41. Miltersen, P. B., and Sorensen, T. B. 2007. A Near-Optimal Strategy for a Heads-Up No-Limit Texas Hold'em Poker Tournament. In Proceedings of the Sixth International Conference on Autonomous Agents and MultiAgent Systems (AAMAS 2007). Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
42. Miltersen, P. B., and Sørensen, T. B. 2006. Computing Proper Equilibria of Zero-Sum Games. In Proceedings of the 5th International Conference on Computers and Games. Lecture Notes in Computer Science. Berlin: Springer-Verlag.
43. Moreno, D., and Wooders, J. 1996. Coalition-Proof Equilibrium. Games and Economic Behavior 17(1): 80-112. (Pubitemid 126164734)
44. Nemhauser, G., and Wolsey, L. 1999. Integer and Combinatorial Optimization. John Wiley & Sons.
45. Nesterov, Y. 2005a. Excessive Gap Technique in Nonsmooth Convex Minimization. SIAM Journal of Optimization 16(1): 235-249. (Pubitemid 43268550)
46. Nesterov, Y. 2005b. Smooth Minimization of NonSmooth Functions. Mathematical Programming 103:127-152.
47. Ray, I. 1996. Coalition-Proof Correlated Equilibrium: A Definition. Games and Economic Behavior 17(1): 56-79.
48. Romanovskii, I. 1962. Reduction of a Game with Complete Memory to a Matrix Game. Soviet Mathematics 3: 678-681.
49. Sandholm, T. 2007. Perspectives on Multiagent Learning. Artificial Intelligence 171(7): 382-391. (Pubitemid 46802424)
50. Schnizlein, D.; Bowling, M.; and Szafron, D. 2009. Probabilistic State Translation in Extensive Games with Large Action Sets. In Proceedings of the 21st International Joint Conference on Artificial Intelligence (IJCAI-2009). Menlo Park, CA: AAAI Press.
51. Shi, J., and Littman, M. 2002. Abstraction Methods for Game Theoretic Poker. In Revised Papers from the Second International Conference on Computers and Games, Lecture Notes in Computer Science, 333-345. Berlin: Springer- Verlag.
52. Sklansky, D. 1999. The Theory of Poker, fourth edition. Las Vegas, NV: Two Plus Two Publishing.
53. Southey, F.; Bowling, M.; Larson, B.; Piccione, C.; Burch, N.; Billings, D.; and Rayner, C. 2005. Bayes' Bluff: Opponent Modelling in Poker. In Proceedings of the 21st Annual Conference on Uncertainty in Artificial Intelligence (UAI 2005), 550-558. Redmond, WA: AUAI Press.
54. von Stengel, B. 1996. Efficient Computation of Behavior Strategies. Games and Economic Behavior 14(2): 220-246. (Pubitemid 126169180)
55. Waugh, K.; Bard, N.; and Bowling, M. 2009. Strategy Grafting in Extensive Games. In Proceedings of the 23rd Annual Conference on Neural Information Processing Systems (NIPS 2009). Cambridge, MA: The MIT Press
56. Waugh, K.; Schnizlein, D.; Bowling, M.; and Szafron, D. 2009a. Abstraction Pathologies in Extensive Games. In Proceedings of the 8th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS 2009). Richland, SC: International Foundation for Autonomous Agents and Multiagent Systems.
57. Waugh, K.; Zinkevich, M.; Johanson, M.; Kan, M.; Schnizlein, D.; and Bowling, M. 2009b. A Practical Use of Imperfect Recall. In Proceedings of the 8th Symposium on Abstraction, Reformulation and Approximation (SARA2009). Menlo Park, CA: AAAI Press.
58. Wellman, M. 2006. Methods for Empirical Game-Theoretic Analysis (Extended Abstract). In Proceedings of the 21st AAAI Conference on Artificial Intelligence (AAAI-2006), 1552-1555. Menlo Park, CA: AAAI Press. Menlo Park, CA: AAAI Press.
59. Zinkevich, M.; Bowling, M.; Johanson, M.; and Piccione, C. 2007. Regret Minimization in Games with Incomplete Information. In Proceedings of the Twenty-First Annual Conference on Neural Information Processing Systems (NIPS 2007). Cambridge, MA: The MIT Press.