Auctioning the right to choose when competition persists

Several papers compare auctioning heterogeneous assets sequentially with sequentially selling the right to choose among assets not yet taken. Typically motivated by auctions of condos for owner occupation, these papers have assumed that each winning bidder exits, so each successive auction has less competition. In many heterogeneous-asset-sale situations, a winning bidder may still be interested in acquiring further assets. We build a simple model of persistent competition, in which the distribution of equilibrium revenue from separate sales is shown to be a mean-preserving spread of the distribution of revenue from selling rights to choose. Persistent competition reveals that a high bidder does not always select his most preferred asset, and that one asset being slightly more likely to be a favored asset discontinuously affects equilibrium bidding.