Ian Gale

Standard Auctions with Financially Constrained Bidders

We develop a methodology for analyzing the revenue and efficiency performance of auctions when buyers have private information about their willingness to pay and ability to pay. We then apply the framework to scenarios involving standard auction mechanisms. In the simplest case, where bidders face absolute spending limits, first-price auctions yield higher expected revenue and social surplus than second-price auctions. The revenue dominance of first-price auctions over second-price auctions carries over to the case where bidders have access to credit. These rankings are explained by differences in the extent to which financial constraints bind in different auction formats.

The Optimal Mechanism for Selling to a Budget-Constrained Buyer

This paper finds an optimal mechanism for selling an indivisible good to consumers who may be budget-constrained. Unlike the case where buyers are not budget constrained, a single posted price is not typically optimal. An optimal mechanism generally consists of a continuum of lotteries indexed by the probability of comsumption and the entry fee.

The efficiency of advance-purchase discounts in the presence of aggregate demand uncertainty

Abstract The pricing behavior of two airlines is examined - one is operated by a welfare-maximizing social planner, the other by an unregulated monopolist. Total capacity is fixed and aggregate demand is uncertain. It is shown that advance-purchase discounts can assist in attaining an efficient allocation of capacity when it is not feasible to operate a spot market on the day of the flight. It is further shown that the planner may offer larger or smaller discounts than the monopolist.

Rent dissipation when rent seekers are budget constrained

In the original Tullock (1975, 1980) game, an individual bidders probability of winning with a bid b is proportional to bR, where the exponent reflects economies of scale in rent seeking. Different interpretations can be given to these probabilities. First, one may view R as a reflection of the political culture. Alternatively, one may view R as a choice variable for a politician. Intuition suggests that a society with a high tolerance for the selling of political favors and politicians who are receptive to rent seeking would both induce greater rent-seeking expenditures than other societies, all else equal. This paper shows that a lower value of R can actually lead to more rent dissipation than a higher value. This paper also reinforces two points concerning rent seeking. First, the analysis confirms the robustness of under-dissipation of rents, even in the face of entry. Second, it points out the importance of distinguishing between rent-seeking expenditures and rent dissipation. When bidders must borrow, for example, total expenditure may understate rent dissipation.

Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints

We show that all-pay auctions dominate first-price sealed-bid auctions when bidders face budget constraints. This ranking is explained by the fact that budget constraints bind less frequently in the all-pay auctions, which leads to more aggressive bidding in that format.

Price Dispersion in a Market with Advance Purchases

This paper examines price discrimination in a market where consumers learn their preferences over time. The products are perfect substitutesex ante, but there is horizontal differentiationex post. Air travel provides one example of such a market. In equilibrium, there is more price discrimination under duopoly than under monopoly, which is consistent with recent empirical evidence from the U.S. airline industry.

Sequential Auctions of Endogenously Valued Objects

Two completely informed but possibly asymmetric bidders buy or sell identical “claims” in sequential auctions. They subsequently receive monetary prizes that depend upon the final allocation of claims. Iterated elimination of weakly dominated strategies leaves a unique Nash equilibrium. For any prize schedule, prices weakly decline as the auctions progress, and points of strict decline have a simple characterization. For one class of prize schedules, which arises naturally if duopolists bid for a scarce input, the equilibrium is completely characterized; many initial allocations generate the same final (unequal) division of claims, which may be interpreted as the natural market structure. Journal of Economic Literature Classification Numbers: D43, D44, L11.

Sequential Procurement With Subcontracting

Two symmetric sellers are approached sequentially by fragmented buyers. Each buyer conducts a second-price auction and purchases from the seller who offers the lower price. Winning an auction affects bidding for future contracts because the sellers have nonconstant marginal costs. We assume that the sellers are completely informed, and we study the unique equilibrium that survives iterated elimination of weakly dominated strategies. If subcontracting between the sellers is impossible, the final allocation of contracts is generally inefficient. If postauction subcontracting is possible, the sellers can be worse off, ex ante, than when subcontracting is impossible.

Revenue comparisons for auctions when bidders have arbitrary types

This paper develops a methodology for characterizing expected revenue from auctions when bidders’ types come from an arbitrary distribution. In particular, types may be multidimensional, and there may be mass points in the distribution. One application extends existing revenue equivalence results. Another application shows that first-price auctions yield higher expected revenue than second-price auctions when bidders are risk averse and facefinancial constraints. This revenue ranking extends to risk-averse bidders with general forms of nonexpected utility preferences.

Price competition in noncooperative joint ventures

Abstract Firms that participate in a cotenancy joint venture are able to utilize capacity that is left unused by other firms. This paper considers a cotenancy involving two or more firms. In equilibrium, the firms quote prices that are socially optimal given the level of aggregate capacity. When there is open entry, the resulting (common) equilibrium price converges to the Ramsey optimal price. A cotenancy may be of use as an alternative to direct regulation of a natural monopoly or as an antitrust remedy, as it combines the benefits of single plant production with competition at the marketing stage.