Infinite games with finite knowledge gaps

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow. Instead, our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play. We show that it is decidable whether a given game satisfies the condition, and prove tight complexity bounds for the strategy synthesis problem under $\omega$-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio

A Perfect-Information Construction for Coordination in Games

We present a general construction for eliminating imperfect information from games with several players who coordinate against nature, and to transform them into two-player games with perfect information while preserving winning strategy profiles. The construction yields an infinite game tree with epistemic models associated to nodes. To obtain a more succinct representation, we define an abstraction based on homomorphic equivalence, which we prove to be sound for games with observable winning conditions. The abstraction generates finite game graphs in several relevant cases, and leads to a new semi-decision procedure for multi-player games with imperfect information