Games with Imperfect Information
Jean R. S. Blair, David Mutchler, Cheng Liu · The MIT Press eBooks · 2014
An information set in a game tree is a set of nodes from which the rules of the game require that the same alternative (i.e., move) be selected. Thus the nodes an information set are indistinguishable to the player moving from that set, thereby reflecting imperfect in-formation, that is, information hidden from that player. Information sets arise naturally in (for example) card gaines like poker and bridge. IIere we focus not on the solution concept for im-perfect information games (which has been studied at length), but rather on the computational aspects of such games: how hard is it to compute solutions? We present two fundainental results for imperfect informa-tion games. The first result shows that even if there is only a single player, we must seek special cases or heuristics. The second result complements the first, providing an efficient algorithm for just such a special case. Additionally, we show how our special case algo-rithm can be used as a heuristic in the general case. 1