Behavior-like Strategies for Games without Perfect Recall

We seek sets of mixed strategies for a player in an extensive form game such that 1. the set has the same power as the set of all mixed strategies, 2. the set is described by a small number of variables, 3. the probability that the player will follow a particular path in the game tree is a linear function of the variables, 4. there is a simple method of randomly picking a pure strategy as specified by a mixed strategy from the set. It is known how to do this for players with perfect recall using behavior strategies [2] and path probabilities [3, 4, 5, 7]. We generalize these techniques to apply to players without perfect recall. The number of variables depends on the closeness of the players to perfect recall or to the amount of corelation needed. We give techniques whereby our more general realization plans can be derived from the game tree.