Risk-neutral sellers can extract high profits from risk-loving buyers by selling them lotteries. To limit risk-taking, gambling is heavily regulated in most countries. I show that protecting risk-loving buyers is essentially impossible.
Even if buyers are risk-loving only asymptotically, the seller can construct a non-random winner-pays auction that ensures unbounded profits. Buyers are asymptotically risk-loving, for example, when their preferences satisfy Savage's axioms or they have cumulative prospect theory preferences. The profits are unbounded even if the seller cannot use any mechanism that resembles a lottery. Asymptotically risk-loving preferences are both sufficient and necessary for unbounded profits.
I study a repeated mechanism design problem where a revenue-maximizing monopolist sells a fixed number of service slots to randomly arriving buyers with private values and increasing exit rates.
In addition to characterizing the fully optimal mechanism, I study the optimal mechanisms in two restricted classes. First, the pure calendar mechanism, where the seller allocates future service dates instead of general promises. The unique optimal pure calendar mechanism is characterized in terms of the opportunity costs of allocating additional service slots. Second, I analyze the waiting list mechanism, where promises of delayed service can depend on future arrivals, but the seller cannot discriminate among buyers who are offered the same position in the waiting list. Both the waiting list and the fully optimal mechanism are implemented by non-standard auctions with a scoring rule where the distance between buyers' bids affects the allocation. A novel property of these auctions is that for buyers it is better to win by a close margin and it is worse to lose by a close margin. Finally, I model partial commitment power as a penalty that the seller has to pay when forfeiting a promise. All the results are given for general partial commitment and therefore include full commitment and no commitment as special cases.
We consider optimal pricing policies for airlines when passengers are
uncertain at the time of ticketing of their eventual willingness to pay for
air travel. Auctions at the time of departure efficiently allocate space and a
profit maximizing airline can capitalize on these gains by overbooking flights
and repurchasing excess tickets from those passengers whose realized value is
low. Nevertheless profit maximization entails distortions away from the
efficient allocation. Under standard regularity conditions we show that the
optimal mechanism can be implemented by a modified double auction.
In order to encourage early booking, passengers who
purchase late are disadvantaged. In order to capture the information rents of
passengers with high expected values, ticket repurchases at the time of
departure are at a subsidized price, sometimes leading to unused capacity.
First version: May 2009
From 2012-2014 was circulated under the title "Penny Auctions are Unpredictable
I study penny auctions, a novel auction format where every bid increases the price by a small amount but placing a bid is costly. Outcomes of real-life penny auctions are surprising. Even when selling cash, the seller can get revenue that is much higher or lower than its nominal value, and losers in an auction sometimes pay much more than the winner.
In this article, I characterize all symmetric Markov-perfect equilibria of penny auctions and study penny auctions' properties. I conclude that the high variance of outcomes is a natural property of the penny auction format.