Games with Imperfect Information

Jean R. S. Blair, David Mutchler and Ching Liu

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 in an information set are indistinguishable to the player moving from that set, thereby reflecting IMPERFECT INFORMATION, that is, information hidden from that player. Information sets arise naturally in (for example) card games like poker and bridge. Here we focus not on the solution concept for imperfect 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 fundamental results for imperfect information 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 algorithm can be used as a heuristic in the general case.

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