Editing Strategy (game theory) (section)

=== Strategy with perfect recall ===
{{Main articles|Perfect recall (game theory)}}
Perfect recall is defined as the ability of every player in game to remember and recall all past actions within the game. Perfect recall is required for equivalence as, in finite games with imperfect recall, there will be existing mixed strategies of Player I in which there is no equivalent behavior strategy. This is fully described in the ''Absent-Minded Driver'' game formulated by Piccione and Rubinstein. In short, this game is based on the decision-making of a driver with imperfect recall, who needs to take the second exit off the highway to reach home but does not remember which intersection they are at when they reach it. Figure [2] describes this game.

Without perfect information (i.e. imperfect information), players make a choice at each decision node without knowledge of the decisions that have preceded it. Therefore, a player’s mixed strategy can produce outcomes that their behavioral strategy cannot, and vice versa. This is demonstrated in the ''Absent-minded Driver'' game. With perfect recall and information, the driver has a single pure strategy, which is [continue, exit], as the driver is aware of what intersection (or decision node) they are at when they arrive to it. On the other hand, looking at the planning-optimal stage only, the maximum payoff is achieved by continuing at both intersections, maximized at p=2/3 (reference). This simple one player game demonstrates the importance of perfect recall for outcome equivalence, and its impact on normal and extended form games.<ref>{{Cite arXiv|last=Kak|first=Subhash|date=2017|title=The Absent-Minded Driver Problem Redux|class=cs.AI |eprint=1702.05778 }}</ref>