We consider two-player combinatorial games in which the graph of positions is random and perhaps infinite, focusing on directed Galton-Watson trees. As offspring distribution varied, a game can undergo phase transition, probability draw under optimal play becomes positive. study nature transitions occur for normal rules (where player unable to move loses game) misere wins), as well an escape on...

Our paper is actually two contributions in one. First, we argue that IBM’s Jeopardy! playing machine needs a formal semantics. We present several arguments as we discuss the system. We also situate the work in the broader context of contemporary AI. Our second point is that the work in this area might well be done as a broad collaborative project. Hence our “Blue Sky” contribution is a proposal...