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When bidders have a common value or strongly affiliated values for an object or contract being auctioned by sealed bids, it is possible that the maker of a rational and apparently winning bid would, upon learning the competing bids, prefer losing the auction to honoring his bid. The ability to withdraw a bid, perhaps at a cost, in such circumstances provides a form of “winner's curse insurance.” Bidding with such insurance is analyzed, obtaining the general condition for rational bid withdrawal and sufficient conditions for the existence of an equilibrium with more aggressive bidding. Next, we define a “compensation penalties” bid withdrawal penalty scheme and show that with it the bid-taker is better off on the average than if bid withdrawal is impossible. Finally, we find equilibrium bidding and withdrawal strategies in a multiplicative model as a function of the magnitude of the bid withdrawal penalty and of the bid-taker's likelihood, after a withdrawal, of honoring the second-best bid. This model has cases in which allowing withdrawal at a cost is in the bid-taker's interest and ones in which it is not.
Harstad et al. (Fri,) studied this question.