Private monitoring in auctions

We study infinitely repeated first-price auctions in which a bidder only learns whether or not he won the object. While repetition of the stage-game equilibrium is the unique Nash equilibrium in public strategies, with patient bidders there are simple Nash equilibria in private strategies that improve on bid rotation. Sequential rationality is appropriately captured by essentially perfect Bayesian equilibrium (EPBE), which ignores behavior after irrelevant histories. Our main result is the construction of EPBEa that improve upon bid rotation. Assuming symmetry, the exclusionary schemes of Skrzypacz and Hopenhayn [Tacit collusion in repeated auctions, J. Econ. Theory 114 (2004), 153-169], including asymptotically efficient ones, are supported as EPBEa.