Public Information Representation for Adversarial Team Games

The study of sequential games in which a team plays against an adversary is receiving an increasing attention in the scientific literature. Their peculiarity resides in the asymmetric information available to the team members during the play which makes the equilibrium computation problem hard even with zero-sum payoffs. The algorithms available in the literature work with implicit representations of the strategy space and mainly resort to Linear Programming and column generation techniques. Such representations prevent from the adoption of standard tools for the generation of abstractions that previously demonstrated to be crucial when solving huge two-player zero-sum games. Differently from those works, we investigate the problem of designing a suitable game representation over which abstraction algorithms can work. In particular, our algorithms convert a sequential teamgame with adversaries to a classical two-player zero-sum game. In this converted game, the team is transformed into a single coordinator player which only knows information common to the whole team and prescribes to the players an action for any possible private state. Our conversion enables the adoption of highly scalable techniques already available for two-player zero-sum games, including techniques for generating automated abstractions. Because of the NP-hard nature of the problem, the resulting Public Team game may be exponentially larger than the original one. To limit this explosion, we design three pruning techniques that dramatically reduce the size of the tree. Finally, we show the effectiveness of the proposed approach by presenting experimental results on Kuhn and Leduc Poker games, obtained by applying state-of-art algorithms for two players zero-sum games on the converted games.