Team Correlated Equilibria in Zero-Sum Extensive-Form Games via Tree Decompositions

Despite the many recent practical and theoretical breakthroughs in computational game theory, equilibrium finding extensive-form team games remains a significant challenge. While NP-hard worst case, there are provably efficient algorithms for certain families of game. In particular, if has common external information, also known as A-loss recall---informally, actions played by non-team members (i.e., opposing or nature) either unknown to entire team, knowledge within team---then polynomial-time exist. this paper, we devise completely new algorithm solving games. It uses tree decomposition constraint system representing each team's strategy reduce number degree constraints required correctness (tightness mathematical program). Our approach bags correspond team-public states---that is, minimal sets nodes (that states team) such that, upon reaching set, it is among players on that set been reached. reduces problem linear program with at most O(NW^(w+1)) nonzero entries matrix, where N size tree, w parameter depends amount uncommon W treewidth decomposition. public-action games, our bounded tighter 2^(O(nt))N teams n t types each. based way write custom, concise decomposition, its fast run time does not assume small treewidth. Since describes polytope correlated strategies directly, get free---instead of, say, having double oracle algorithm. We show via experiments standard suite achieves state-of-the-art performance all benchmark classes except one. present, knowledge, first setting both have more than one member.