Optimal reserve prices in sealed-bid auctions with reference effects

The reference effect and loss aversion are incorporated into the buyer’s utility in the symmetric independent private value models of sealed-bid auctions. The buyer’s equilibrium bidding strategy and the seller’s optimal reserve price are derived for the first-price and second-price sealed-bid auctions. In both auction mechanisms, the seller’s optimal reserve price and expected revenue are increasing in the reference point. We compare the seller’s expected revenues as well as the optimal reserve prices in the two auctions. The results show that the seller will set a higher optimal reserve price but obtain lower optimal expected revenue in the second-price auction compared to the first-price auction. Further, we extend the model to the gain-seeking case, and endogenize the reference point as the ex-ante expected price of the item in equilibrium. In contrast to the loss-averse case, the seller will set a lower optimal reserve price but obtain higher optimal expected revenue in the second-price auction compared to the first-price auction if the buyers are gain-seeking. With an endogenous reference point, similar results are obtained in terms of revenue comparison between the two auctions.     

Optimal bid disclosure in patent license auctions under alternative modes of competition

The literature on patent license auctions in oligopoly assumed that the auctioneer reveals the winning bid and stressed that this gives firms an incentive to bid high in order to signal an aggressive output strategy in a downstream Cournot market game, and conversely bid low to signal acquiescent pricing in a Bertrand market game. The present paper examines the information revealed by publishing the winning or the losing or no bid, assuming an oligopoly with differentiated goods. We rank disclosure rules and find that it is not optimal for the innovator to disclose the winning bid, regardless of the mode of competition.     

Position auctions

I analyze the equilibria of a game based on the ad auction used by Google and Yahoo. This auction is closely related to the assignment game studied by Shapley–Shubik, Demange–Gale–Sotomayer and Roth–Sotomayer. However, due to the special structure of preferences, the equilibria of the ad auction can be calculated explicitly and some known results can be sharpened. I provide some empirical evidence that the Nash equilibria of the position auction describe the basic properties of the prices observed in Google's ad auction reasonably accurately.     

Penny auctions

This paper studies penny auctions, a novel auction format in which every bid increases the price by a small amount, but placing a bid is costly. Outcomes of real-life penny auctions are often surprising. Even when selling cash, the seller may obtain revenue that is much higher or lower than its nominal value, and losers in an auction sometimes pay much more than the winner. This paper characterizes all symmetric Markov-perfect equilibria of penny auctions and studies penny auctions’ properties. The results show that a high variance of outcomes is a natural property of the penny auction format and high revenues are inconsistent with rational risk-neutral participants.     

Optimal organization in a sequential investment problem with the principal's cancellation option

This paper considers a two-stage sequential investment problem where the principal wishes to cancel the project if it fails in the first stage. Suppose that only the first-stage agent can observe the outcome in the first stage. There are two organizational forms to choose from: integration, where a single agent is in charge of investments in two stages; and separation, where two different agents are in charge of the two stages. Integration gives rise to a smaller wage cost of inducing high effort in both stages; however, in order to obtain the correct information to cancel the project, separation may have some advantage in terms of saving the information rent. We show that when the effort cost in the first stage is sufficiently small, the principal prefers separation because the first-stage agent has less incentive to lie about the outcome.     

Resale and bundling in auctions

The possibility of resale increases bidders' incentives to jointly reduce demand in multi-object auctions, because resale increases low-value bidders' willingness to pay and reduces high-value bidders' willingness to pay. Therefore, resale may reduce the seller's revenue. In a simple model with complete information, however, allowing resale and bundling the objects on sale are “complement strategies” for the seller (under reasonable conditions)—by bundling and allowing resale the seller earns a higher revenue than by selling the objects separately and/or forbidding resale. We also show why allowing resale may reduce efficiency.     

Position auctions with dynamic resizing

This paper analyzes mechanisms for selling advertising inventory in a position auction in which displaying less than the maximal number of ads means the ads that are shown can be dynamically resized and displayed more prominently. I characterize the optimal mechanism with and without dynamic resizing, and illustrate how the optimal reserve prices in a Vickrey–Clarke–Groves mechanism vary with the amount of dynamic resizing and the number of bidders.     

Optimality of simple procurement auctions

We consider procurement auctions for the projects where the cost of production is subject to ex-post shocks—cost overruns. The contractor may default due to these overruns, which affects the buyer’s expected cost. Here the lowest-bid auction emerges as the procurement mechanism that: (i) minimizes the expected transfers to the contractors, and (ii) requires the lowest surety bond to achieve a given probability of default. Since surety bonds are costly to post, the above makes a combination of the lowest-bid auction with the surety bond the optimal, i.e., the expected cost minimizing procurement mechanism in a wide range of parameters.     

Hiccups in US spectrum auctions

While an increasing number of countries have embraced auctions to assign radio frequency, many other countries have decided to retain selection by the administration. Of the many factors that might have influenced those countries that have rejected auctions, one of the most visible in Europe has been frequent media reports of the problems experienced with auctions in the US between 1995 and 1997. In my experience, these reports have been accepted at face value by many European industry commentators and policy officials. It seems clear that the repeated reporting of these problems has influenced the evolution of spectrum management policy in Europe. This paper tries to set the record straight by providing an analysis of the problems that were reported in Europe regarding US spectrum auctions, specifically the declarations of bankruptcy by several winning bidders and overbidding by participants, the enormous revenue shortfall on the WCS block auction, and reports of collusion among bidders.     

Information disclosure in optimal auctions

This paper analyzes a situation in which the seller controls the accuracy of what potential buyers learn about their valuation of a good to be sold. This setting is related to many real situations such as home sales, antique auctions, and digital platforms such as Google and Facebook selling online advertising slots. Two important questions arise: what is the optimal selling mechanism, and what is the optimal disclosure policy of the seller. Under the assumption of private values, a simple auction with a reserve price is the optimal mechanism. What we show is that the amount of (costly) information provided increases with the number of potential bidders when using the optimal mechanism and is greater than when the object is always sold. Because information changes the distribution of a bidder’s expected valuations, the optimal reserve price also changes, so that the number of bidders (indirectly) affects the reserve price. We show that as the number of bidders increases, the optimal reserve price becomes more restrictive.     

Reverse auctions for relationship marketers

Reverse auctions in logistics and procurement have grown dramatically since the advent of widespread Internet usage in the late 1990s. A literature review indicates that scholars and practitioners are reaching a consensus around a trade-off between the value and benefits of gaining lower prices versus losing long-term relationships with suppliers. Yet at the same time, a quiet evolution has come about in the economics and management literature, opening the way for new, more relationship-friendly auction designs. Based on this new work, a series of guidelines and principles are developed which describe how managers may collect the economic pricing advantage of reverse auctions—yet retain the long-term benefits of relationship marketing.     

Procurement auctions with entry of bidders

In procurement auctions with a fixed number of bidders there is a tradeoff between cost efficiency and rent extraction. An optimal mechanism, therefore, entails distortions of effort (Laffont and Tirole, 1987). If potential suppliers must sink an entry investment before they can participate in the auction, then decreasing the firms' rent may imply reduced entry. We show that if potential bidders are uninformed before entry, commitment to a plain, nondistortive auction is optimal. In contrast, if potential bidders learn all their private information before entry, the optimal mechanism entails the same distortions as in Laffont and Tirole's static model.     

Secret reserve prices in first-price auctions

This article offers a theoretical explanation for the use of secret reserve prices in auctions. I study first-price auctions with and without secret reserve price in an independent private values environment with risk-neutral buyers and a seller who cares at least minimally about risk. The seller can fix the auction rules either before or after she learns her reservation value. Fixing the rules early and keeping the right to set a secret reserve price can be strictly optimal. Moreover, I describe the relation of using a secret reserve price to phantom bidding and non-commitment to sell.     

Securities auctions with pre-project information management

This paper analyzes securities auctions in which bidders have an option to acquire information after winning the right to develop a project. The payment consists of an up-front cash bid and a contingent security bid, which distorts investment and information acquisition relative to the first-best. We order securities in terms of their steepness: the payment of a steeper security is more sensitive to high project values. The agent’s incentives to acquire information that prevents either cost overruns (Type I errors) or false cancellations (Type II errors) decrease with the steepness of securities. The optimal limited-liability securities auction involves bidding debt that minimizes the distortions in the agent’s incentives to acquire performance-enhancing information. The model delivers implications on the practices commonly observed in oil lease auctions.     

Entry into auctions: An experimental analysis

This paper investigates entry decisions into first and second-price auctions using an experimental design to extract information on willingness-to-pay to enter (WTE). We find that subjects tend to overpay to enter both auction formats. In particular, if the subjects believe they will be bidding against bidders following the risk-neutral Nash strategy, their WTE is greater than the optimal risk-neutral amount 97% of the time for first-price auctions (FPA) and 90% for second-price auctions (SPA). If they believe that they are bidding against subjects who bid as do the other subjects, they submit a WTE that is too high 92% of the time for FPA and 69% of the time for SPA. We also find, in line with previous studies, significant overbidding in both the FPA and SPA. We then investigate whether introducing risk aversion (RA) or “joy of winning” (JOY) can explain the joint observation of over-entry and overbidding. In particular, using bid data alone, we structurally estimate three models, one allowing RA only, one allowing for JOY only and one allowing for both RA and JOY. While a model with JOY alone overestimates WTE, we find that RA alone can explain 38% of WTE but a model with both RA and JOY (where RA is estimated using FPA bids, and JOY is estimated using SPA bids) can explain 65% of WTE. Moreover, JOY appears to explain nearly all of the male WTE but only 44% of the female WTE.     

Synergistic valuations and efficiency in spectrum auctions

In spectrum auctions, bidders typically have synergistic values for combinations of licenses. This has been the key argument for the use of combinatorial auctions in the recent years. Considering synergistic valuations turns the allocation problem into a computationally hard optimization problem that generally cannot be approximated to a constant factor in polynomial time. Ascending auction designs such as the Simultaneous Multiple Round Auction (SMRA) and the single-stage or two-stage Combinatorial Clock Auction (CCA) can be seen as simple heuristic algorithms to solve this problem. Such heuristics do not necessarily compute the optimal solution, even if bidders are truthful. We study the average efficiency loss that can be attributed to the simplicity of the auction algorithm with different levels of synergies. Our simulations are based on realistic instances of bidder valuations we inferred from bid data from the 2014 Canadian 700 MHz auction. The goal of the paper is not to reproduce the results of the Canadian auction but rather to perform “out-of-sample” counterfactuals comparing SMRA and CCA under different synergy conditions when bidders maximize payoff in each round. With “linear” synergies, a bidder's marginal value for a license grows linearly with the total number of licenses won, while with the “extreme national” synergies, this marginal value is independent of the number of licenses won unless the bidder wins all licenses in a national package. We find that with the extreme national synergy model, the CCA is indeed more efficient than SMRA. However, for the more realistic case of linear synergies, SMRA outperforms various versions of CCA that have been implemented in the field including the one used in the Canadian 700 MHz auction. Overall, the efficiency loss of all ascending auction algorithms is small even with high synergies, which is remarkable given the simplicity of the algorithms.     

Spectrum auctions in India: lessons from experience

Spectrum auctions have been used with significant success in many developed countries. From a regulatory and policy perspective, spectrum auctions ensure the efficient use of spectrum by allocating it to those entities that value it most, while also generating revenues for governments. But auctions may lead to unexpected outcomes due to unanticipated problems with their design leading to unexpected bidder behavior such as collusion and over-bidding. The key challenge before regulatory agencies is to design auctions in such a way as to meet the objective of fostering competition while at the same time ensuring that bidders can effectively use the spectrum for their business. While India was one of the early adopters of spectrum auctions, its success in service provision has been low. This paper critically examines issues in auction design that contributed to this delay and reviews the key elements in the design process namely a coherent regulatory framework, choice of service areas, flexibility for service area consolidation, standards and their role, convergence, managing public service regulation and managing defaults. The paper compares the handling of these elements in auctions in the United States (US), United Kingdom (UK) and Australia with the objective of drawing lessons for Indian policy makers.     

Comparing predicted prices in auctions for online advertising

Online publishers sell opportunities to show ads. Some advertisers pay only if their ad elicits a user response. Publishers estimate response rates for ads in order to estimate expected revenues from showing the ads. Then publishers select ads that maximize estimated expected revenue.By taking a maximum among estimates, publishers inadvertently select ads based on a combination of actual expected revenue and inaccurate estimation of expected revenue. Publishers can increase actual expected revenue by selecting ads to maximize a combination of estimated expected revenue and estimation accuracy.     

Affirmative action subcontracting regulations in dynamic procurement auctions

I study affirmative action subcontracting regulations in a model where governments use auctions to repeatedly procure goods and services at the lowest possible price. Through using disadvantaged subcontractors, prime contractors build relationships over time, resulting in lower subcontracting costs in future periods. I find that regulation in the form of a minimum subcontracting requirement expands bidder asymmetries, favoring prime contractors with stronger relationships over those with weaker ones. Simulations show that the manner in which relationships evolve determines not only the utilization of disadvantaged subcontractors but also the procurement costs attained under affirmative action.     

Fighting collusion in auctions: An experimental investigation

The danger of collusion presents a serious challenge for auctioneers. In this paper, we compare the collusive properties of two standard auctions, the English auction and the first-price sealed-bid auction, and a lesser-known format, the Amsterdam (second-price) auction. In the Amsterdam auction, the highest losing bidder earns a premium for stirring up the price. We study two settings: in one, all bidders can collude, and in another, only a subset is eligible. The experiments show that the Amsterdam auction triggers less collusion than the standard auctions. We compare experimental results to theoretical predictions, and provide an explanation where they differ.