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We focus on the problem of finding an optimal strategy for a team of twoplayers that faces an opponent in an imperfect-information zero-sumextensive-form game. Team members are not allowed to communicate during playbut can coordinate before the game. In that setting, it is known that the bestthe team can do is sample a profile of potentially randomized strategies (oneper player) from a joint (a.k.a. correlated) probability distribution at thebeginning of the game. In this paper, we first provide new modeling resultsabout computing such an optimal distribution by drawing a connection to adifferent literature on extensive-form correlation. Second, we provide analgorithm that computes such an optimal distribution by only using profileswhere only one of the team members gets to randomize in each profile. We canalso cap the number of such profiles we allow in the solution. This begets ananytime algorithm by increasing the cap. We find that often a handful ofwell-chosen such profiles suffices to reach optimal utility for the team. Thisenables team members to reach coordination through a relatively simple andunderstandable plan. Finally, inspired by this observation and leveragingtheoretical concepts that we introduce, we develop an efficientcolumn-generation algorithm for finding an optimal distribution for the team.We evaluate it on a suite of common benchmark games. It is three orders ofmagnitude faster than the prior state of the art on games that the latter cansolve and it can also solve several games that were previously unsolvable.

Faster Algorithms for Optimal Ex-Ante Coordinated Collusive Strategies in Extensive-Form Zero-Sum Games