Prior-free multi-unit auctions with ordered bidders

Prior-free auctions are robust auctions that assume no distribution over bidders' valuations and provide worst-case (input-by-input) approximation guarantees. In contrast to previous work on this topic, we pursue good prior-free auctions with non-identical bidders. Prior-free auctions can approximate meaningful benchmarks for non-identical bidders only when sufficient qualitative information about the bidder asymmetry is publicly known. We consider digital goods auctions where there is a total ordering of the bidders that is known to the seller, where earlier bidders are in some sense thought to have higher valuations. We use the framework of Hartline and Roughgarden (STOC'08) to define an appropriate revenue benchmark: the maximum revenue that can be obtained from a bid vector using prices that are nonincreasing in the bidder ordering and bounded above by the second-highest bid. This monotone-price benchmark is always as large as the well-known fixed-price benchmark , so designing prior-free auctions with good approximation guarantees is only harder. By design, an auction that approximates the monotone-price benchmark satisfies a very strong guarantee: it is, in particular, simultaneously near-optimal for essentially every Bayesian environment in which bidders' valuation distributions have nonincreasing monopoly prices, or in which the distribution of each bidder stochastically dominates that of the next. Even when there is no distribution over bidders' valuations, such an auction still provides a quantifiable input-by-input performance guarantee. In this paper, we design a simple -competitive prior-free auction for digital goods with ordered bidders. We also extend the monotone-price benchmark and our -competitive prior-free auction to multi-unit settings with limited supply

Optimal Competitive Auctions

We study the design of truthful auctions for selling identical items in unlimited supply (e.g., digital goods) to n unit demand buyers. This classic problem stands out from profit-maximizing auction design literature as it requires no probabilistic assumptions on buyers' valuations and employs the framework of competitive analysis. Our objective is to optimize the worst-case performance of an auction, measured by the ratio between a given benchmark and revenue generated by the auction. We establish a sufficient and necessary condition that characterizes competitive ratios for all monotone benchmarks. The characterization identifies the worst-case distribution of instances and reveals intrinsic relations between competitive ratios and benchmarks in the competitive analysis. With the characterization at hand, we show optimal competitive auctions for two natural benchmarks. The most well-studied benchmark $\mathcal{F}^{(2)}(\cdot)$ measures the envy-free optimal revenue where at least two buyers win. Goldberg et al. [13] showed a sequence of lower bounds on the competitive ratio for each number of buyers n. They conjectured that all these bounds are tight. We show that optimal competitive auctions match these bounds. Thus, we confirm the conjecture and settle a central open problem in the design of digital goods auctions. As one more application we examine another economically meaningful benchmark, which measures the optimal revenue across all limited-supply Vickrey auctions. We identify the optimal competitive ratios to be $(\frac{n}{n-1})^{n-1}-1$ for each number of buyers n, that is $e-1$ as $n$ approaches infinity

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.

How to Allocate R&D (and Other) Subsidies: An Experimentally Tested Policy Recommendation

This paper evaluates how R&D subsidies to the business sector are typically awarded. We identify two sources of ine_ciency: the selection based on a ranking of individual projects, rather than complete allocations, and the failure to induce competition among applicants in order to extract and use information about the necessary funding. In order to correct these ine_- ciencies we propose mechanisms that include some form of an auction in which applicants bid for subsidies. Our proposals are tested in a simulation and in controlled lab experiments. The results suggest that adopting our proposals may considerably improve the allocation

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.conservation auctions, Conservation Reserve Program, CRP, bid caps, experimental economics