PPT-Safe and Nested Subgame Solving for Imperfect-Information Games

NIPS 2017 Best Paper Award Noam Brown and Tuomas Sandholm Computer Science Department Carnegie Mellon University ImperfectInformation Games Poker Security Physical and Cyber Negotiation. . Histories and . subhistories. A terminal history is a listing of every play in a possible course of the game, all the way to the end. . A . proper . subhistory. . is a listing of every play in the course of the game up to some point before the end.. Problems from . Ch. 8. The OS2 story. Introduced by IBM in 1987 to compete. with MS Windows.. Faster and more reliable than Windows. but not many applications available.. A Model of Attracting Developers. (. Subgame. perfection with incomplete information ). Econ 171. Subgame. Perfection with Imperfect Information. How can the notion of . subgame. perfection help us if there is incomplete information?. with . Short-Lived Players. 九州. 大学. ジョ・ヨンジュン. Repeated Games and Reputations. Under Construction. Long-lived player (player 1). and short lived player (player 2). 長期. プレイヤ. Extensive-form games with perfect information. Player 1. Player 2. Player 2. Player 1. 2, 4. 5, 3. 3, 2. 1, 0. 0, . 5. Players do not move simultaneously. When moving, each player is aware of all the previous moves (. . Histories and . subhistories. A terminal history is a listing of every play in a possible course of the game, all the way to the end. . A . proper . subhistory. . is a listing of every play in the course of the game up to some point before the end.. if. Lesson. CS1313 Spring 2017. 1. Nested. . if. . Lesson Outline. Nested. if. Lesson . Outline. A Complicated . if. Example #1. A Complicated . if. Example #2. A Complicated . if. Example #3. Noam Brown. Carnegie Mellon University. Computer Science . Department. Review: Imperfect-Information Game Tree. Information . set. 0.3. 0.5. 0.2. 0.5. 0.5. Negotiations, security, poker. P1. P1. P1. C. Case study: . Poker. Tuomas Sandholm. Carnegie Mellon University. Computer Science Department. Sequential imperfect information games. Players face uncertainty about the state of the world . Sequential (and simultaneous) moves. Game theory applies mathematics to competitive situations. Places emphasis on . the decision-making . of the adversaries. Commonly used in business . and economics. 1994 and 2005 Nobel Prizes for Economic Sciences were given for research in game theory. Praveen Paruchuri, Jonathan P. Pearce, Sarit Kraus. Catherine (Ying) Liu, School of Computer Science, University of Waterloo. Outline. Introduction. Problem Definition. DOBSS Approach. Mixed-Integer Quadratic Program. Case study: . Poker. Tuomas Sandholm. Carnegie Mellon University. Computer Science Department. Sequential imperfect information games. Players face uncertainty about the state of the world . Sequential (and simultaneous) moves. The State of Techniques for Solving Large Imperfect-Information Games Tuomas Sandholm Professor Carnegie Mellon University Computer Science Department Also: Machine Learning Department Ph.D. Program in Algorithms, CMU 15-381 and 15-681. Fall 2017. Teachers:. Noam Brown. Tuomas. . Sandholm. What are Games?. Requirements for a . game. :. At least 2 players. Actions available for each player. Payoffs to each player for those actions.