Shill-proof rules in object allocation problems with
money

Abstract:

We consider the object allocation problem with money. The seller owns multiple units of an object, and is only interested in her revenue from an allocation. Each buyer receives at most one unit of the object, and has a quasi-linear utility function with private valuations. We study incentives of the seller to increase her revenue by introducing false-name buyers, i.e., shill bidding. An (allocation) rule is shill-proof if the seller never benefits from introducing false-name buyers. A rule is a binary posted prices rule if there is a profile of posted prices such that whenever a buyer receives the object, she pays either her posted price or zero, and her payment is equal to zero when she does not receive the object. We show that if a rule satisfies shillproofness, strategy-proofness, and non-imposition, then it is a binary posted prices rule. This result shows that the cost of preventing the seller from shill bidding is equivalent to the rigidity of the payment of each buyer, which highlights the difficulty in preventing the seller from shill bidding. It extends to a model of non-quasi-linear utility functions with interdependent valuations.