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Computing Ex Ante Coordinated Team-Maxmin Equilibria in Zero-Sum Multiplayer Extensive-Form Games
Computational game theory has many applications in the modern world in b...
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Coordination in Adversarial Sequential Team Games via Multi-Agent Deep Reinforcement Learning
Many real-world applications involve teams of agents that have to coordi...
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Computational Results for Extensive-Form Adversarial Team Games
We provide, to the best of our knowledge, the first computational study ...
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Computing Strong Game-Theoretic Strategies in Jotto
We develop a new approach that computes approximate equilibrium strategi...
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Team-maxmin equilibrium: efficiency bounds and algorithms
The Team-maxmin equilibrium prescribes the optimal strategies for a team...
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Coarse Correlation in Extensive-Form Games
Coarse correlation models strategic interactions of rational agents comp...
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Competitive Balance in Team Sports Games
Competition is a primary driver of player satisfaction and engagement in...
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Faster Algorithms for Optimal Ex-Ante Coordinated Collusive Strategies in Extensive-Form Zero-Sum Games
We focus on the problem of finding an optimal strategy for a team of two 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 that 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 computes such an optimal distribution by only using profiles where only one of the team members gets to randomize in each profile. We can also cap the number of such profiles we allow 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 relatively 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.
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