Imperfect Recall and Time Inconsistencies: An experimental Test of the Absentminded Driver “Paradox”

Abstract: Absentmindedness is a special case of imperfect recall, in which a single history includes more than one decision node in an information set. Put differently, players, after making a decision, sometimes face it again without recalling having ‘been there before’. Piccione and Rubinstein (1997b) have argued that absentmindedness may lead to time inconsistencies. Specifically, in certain cases, a player’s optimal strategy as calculated when called to choose an action (the action stage) deviates from the optimal strategy as calculated in a preceding planning stage, although preferences remain constant and no new information is revealed between the two stages. An alternative approach assumes that the player maximizes expected payoff in the action stage while considering his actions at other decision nodes to be immutable. With this approach, no time inconsistencies arise. The present paper explores this issue from a behavioral point of view. We elicit participants’ strategies in an experimental game of absentmindedness, separately for a planning stage and an action stage. We find systematic and robust time inconsistencies under four variations of the experiment and using ten different parameterizations of the game. We conclude that real decisions under absentmindedness without commitment are susceptible to time inconsistencies.

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