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Connecting Optimal Ex-Ante Collusion in Teams to Extensive-Form Correlation: Faster Algorithms and Positive Complexity Results
Gabriele Farina · Andrea Celli · Nicola Gatti · Tuomas Sandholm

Wed Jul 21 06:25 AM -- 06:30 AM (PDT) @ None

We focus on the problem of finding an optimal strategy for a team of players that faces an opponent in an imperfect-information zero-sum extensive-form game. Team members are not allowed to communicate during play but can coordinate before the game. In this setting, it is known that the best the team can do is sample a profile of potentially randomized strategies (one per player) from a joint (a.k.a. correlated) probability distribution at the beginning of the game. In this paper, we first provide new modeling results about computing such an optimal distribution by drawing a connection to a different literature on extensive-form correlation. Second, we provide an algorithm that allows one for capping the number of profiles employed in the solution. This begets an anytime algorithm by increasing the cap. We find that often a handful of well-chosen such profiles suffices to reach optimal utility for the team. This enables team members to reach coordination through a simple and understandable plan. Finally, inspired by this observation and leveraging theoretical concepts that we introduce, we develop an efficient column-generation algorithm for finding an optimal distribution for the team. We evaluate it on a suite of common benchmark games. It is three orders of magnitude faster than the prior state of the art on games that the latter can solve and it can also solve several games that were previously unsolvable.

Author Information

Gabriele Farina (Carnegie Mellon University)

I am currently a first-year Ph.D. student in the Computer Science Department at Carnegie Mellon University, where I am fortunate to be advised by Tuomas Sandholm. I am part of the Electronics Marketplaces Lab. I mostly work on Kidney Exchange and Algorithmic Game Theory.

Andrea Celli (Facebook CDS)
Nicola Gatti (Politecnico di Milano)
Tuomas Sandholm (Carnegie Mellon University)

Tuomas Sandholm is Angel Jordan Professor of Computer Science at Carnegie Mellon University. He is Founder and Director of the Electronic Marketplaces Laboratory. He has published over 450 papers. With his student Vince Conitzer, he initiated the study of automated mechanism design in 2001. In parallel with his academic career, he was Founder, Chairman, and CTO/Chief Scientist of CombineNet, Inc. from 1997 until its acquisition in 2010. During this period the company commercialized over 800 of the world's largest-scale generalized combinatorial multi-attribute auctions, with over $60 billion in total spend and over $6 billion in generated savings. He is Founder and CEO of Optimized Markets, Strategic Machine, and Strategy Robot. Also, his algorithms run the UNOS kidney exchange, which includes 69% of the transplant centers in the US. He has developed the leading algorithms for several general classes of game. The team that he leads is the two-time world champion in computer Heads-Up No-Limit Texas Hold’em poker, and Libratus became the first and only AI to beat top humans at that game. Among his many honors are the NSF Career Award, inaugural ACM Autonomous Agents Research Award, Sloan Fellowship, Carnegie Science Center Award for Excellence, Edelman Laureateship, Newell Award for Research Excellence, and Computers and Thought Award. He is Fellow of the ACM, AAAI, and INFORMS. He holds an honorary doctorate from the University of Zurich.

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