Search Equilibrium with Endogenous Recall

In search models, the property of "recall" has heretofore been treated as exogenous, with a distinction made between models with "no recall" and models with "perfect recall." However, an alternative interpretation is that recall is provided by the firms. Then, "perfect recall" corresponds to holding the good forever, while "no recall" corresponds to a refusal to hold the good at all. Imperfect recall is provided if a firm agrees to hold the good for a finite number of periods. We show that the commonly observed practice of holding the good for some length of time, while the customer continues to shop elsewhere, can be an equilibrium strategy.