Endogenous Entry in First-Price Private Value Auctions: the Self-Selection E¤ect

This paper studies the e¤ect of endogenous entry in ...rst-price private value auctions. Subjects decide, simultaneously, whether to participate in an auction, or to claim an outside option payo¤ for not participating. At this stage all subjects know the distribution of possible values, the number of potential entrants, and the amount of the ...xed outside option payment. After entry, each participating bidder privately learns his value for the object and the number of bidders and then submits a sealed bid. The symmetric mixed-strategy equilibrium is ...rst characterized for homogenous risk preferences. The model is then extended to account for heterogenous risk aversion leading to a pure strategy equilibrium: the self-selection e¤ect. Subjects with higher risk tolerance self select their participation in the auction. There is an equilibrium where all subjects use the same ”cut-o¤” value of risk tolerance parameter as entry strategy. After entry the bidding is less aggressive, re‡ecting greater risk tolerance of subjects. The self-selection e¤ect becomes stronger with increase in the outside option or the number of potential bidders. The latter result is counter intuitive, as it implies that the selling price may go down when auction is highly advertised.