Approximately Optimal Mechanism Design: Motivation, Examples, and Lessons Learned

Optimal mechanism design enjoys a beautiful and well-developed theory, and also a number of killer applications. Rules of thumb produced by the field influence everything from how governments sell wireless spectrum licenses to how the major search engines auction off online advertising. There are, however, some basic problems for which the traditional optimal mechanism design approach is ill-suited --- either because it makes overly strong assumptions, or because it advocates overly complex designs. The thesis of this paper is that approximately optimal mechanisms allow us to reason about fundamental questions that seem out of reach of the traditional theory. This survey has three main parts. The first part describes the approximately optimal mechanism design paradigm --- how it works, and what we aim to learn by applying it. The second and third parts of the survey cover two case studies, where we instantiate the general design paradigm to investigate two basic questions. In the first example, we consider revenue maximization in a single-item auction with heterogeneous bidders. Our goal is to understand if complexity --- in the sense of detailed distributional knowledge --- is an essential feature of good auctions for this problem, or alternatively if there are simpler auctions that are near-optimal. The second example considers welfare maximization with multiple items. Our goal here is similar in spirit: when is complexity --- in the form of high-dimensional bid spaces --- an essential feature of every auction that guarantees reasonable welfare? Are there interesting cases where low-dimensional bid spaces suffice?Comment: Based on a talk given by the author at the 15th ACM Conference on Economics and Computation (EC), June 201

License auctions with exit (and entry) options: Alternative remedies for the exposure problem

Inspired by some spectrum auctions, we consider a stylized license auction with incumbents and one entrant. Whereas the entrant values only the bundle of several units (synergy), incumbents are subject to non-increasing demand. The seller proactively encourages entry and restricts incumbent bidders. In this framework, an English clock auction gives rise to an exposure problem that distorts efficiency and impairs revenue. We consider three remedies: a (constrained) Vickrey package auction, an English clock auction with exit option that allows the entrant to annul his bid, and an English clock auction with exit and entry option that lifts the bidding restriction if entry failed

Proving soundness of combinatorial Vickrey auctions and generating verified executable code

Using mechanised reasoning we prove that combinatorial Vickrey auctions are soundly specified in that they associate a unique outcome (allocation and transfers) to any valid input (bids). Having done so, we auto-generate verified executable code from the formally defined auction. This removes a source of error in implementing the auction design. We intend to use formal methods to verify new auction designs. Here, our contribution is to introduce and demonstrate the use of formal methods for auction verification in the familiar setting of a well-known auction

Package Bidding for Spectrum Licenses

The FCC was an innovator in adopting the rules of the simultaneous ascending-price auction for its sales of spectrum licenses. While these rules have performed well in the auctions conducted so far (and would perform even better with the design improvements suggested in our first report), there are two inherent limitations in any design that seeks to assign and price the licenses individually. First, such designs create strategic incentives for bidders interested in multiple licenses that are substitutes to reduce their demands for some of the licenses in order to reduce the final prices of the others; this is the demand reduction problem. Second, even if bidders behave non-strategically, there is a fundamental problem with the basic concept of individual-license pricing when licenses are complementary. In simultaneous ascending-price auctions, from a bidder's perspective this is the exposure problem. A bidder who is unsuccessful in bidding for a large package of licenses may be left with a partial package whose total price cannot be justified in the absence of those complementary licenses it failed to win. This problem is present in any auction mechanism that sells licenses individually, with no opportunity to bid on packages. In this report our task is confined to analyses of the merits of package bidding and the practical problems of implementation. In our next report, we will outline proposals for the details of the procedural rules and other aspects of implementing a practical design, as well as the software development that would be necessary.Auctions; Spectrum Auctions; Multiple-Round Auctions; Efficiency

First-price vs second-price auctions under risk aversion and private affiliated values

Under a specific informational framework, we compare the seller's expected revenue from a first-price auction and a second-price auction when bidders are risk averse and have private affiliated values.auctions, risk aversion, private affiliated values

Matching and Price Competition

We develop a model in which firms set impersonal salary levels before matching with workers. Salaries fall relative to any competitive equilibrium while profits rise by almost as much, implying little inefficiency. Furthermore, the best firms gain the most from the system while wages become compressed. We discuss the performance of alternative institutions and the recent antitrust case against the National Residency Matching Program in light of our results.

Optimal Real-Time Bidding Strategies

The ad-trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey auctions -- throughout the day for buying ad-inventory with the aim of maximizing one or several key performance indicators (KPI). The optimization problems faced by companies building bidding strategies are new and interesting for the community of applied mathematicians. In this article, we introduce a stochastic optimal control model that addresses the question of the optimal bidding strategy in various realistic contexts: the maximization of the inventory bought with a given amount of cash in the framework of audience strategies, the maximization of the number of conversions/acquisitions with a given amount of cash, etc. In our model, the sequence of auctions is modeled by a Poisson process and the \textit{price to beat} for each auction is modeled by a random variable following almost any probability distribution. We show that the optimal bids are characterized by a Hamilton-Jacobi-Bellman equation, and that almost-closed form solutions can be found by using a fluid limit. Numerical examples are also carried out

CONSUMERS' VALUATION OF INSECTICIDE USE RESTRICTIONS: AN APPLICATION TO APPLES

Economic assessments of pesticide regulations typically focus on producer impacts and generally ignore possible changes in product demand. These changes may be nonnegligible if real and/or perceived product attributes change. We measure consumersÂ’' willingness to pay (WTP) for the elimination of one insecticide and also a whole group of insecticides in apple production using a multiple-round Vickrey auction. The data are analyzed using nonparametric statistical tests and a double-hurdle model. Our findings show that consumer perceptions of product attributes change if pesticides are removed from production, and this is reflected in WTP changes. WTP is shown to be income elastic.Consumer/Household Economics, Crop Production/Industries,

The Effective Use of Limited Information: Do Bid Maximums Reduce Procurement Cost in Asymmetric Auctions?

Conservation programs faced with limited budgets often use a competitive enrollment mechanism. Goals of enrollment might include minimizing program expenditures, encouraging broad participation, and inducing adoption of enhanced environmental practices. We use experimental methods to evaluate an auction mechanism that incorporates bid maximums and quality adjustments. We examine this mechanism’s performance characteristics when opportunity costs are heterogeneous across potential participants, and when costs are only approximately known by the purchaser. We find that overly stringent maximums can increase overall expenditures, and that when quality of offers is important, substantial increases in offer maximums can yield a better quality-adjusted result.