25 research outputs found
Empirical relevance of ambiguity in first-price auctions
We study the identification and estimation of first-price auctions with independent private values if bidders face ambiguity about the valuation distribution and have maxmin expected utility. Using variation in the number of bidders we nonparametrically identify the true valuation distribution and the lower envelope of the set of prior beliefs. We also allow for CRRA and unobserved auction heterogeneity, and propose a Bayesian estimation method based on Bernstein polynomials. Monte Carlo experiments show that our estimator performs well, and incorrectly ignoring ambiguity induces bias and loss of revenue. We find evidence of ambiguity in timber auctions in the Pacific Northwest
On the Robustness of Second-Price Auctions in Prior-Independent Mechanism Design
Classical Bayesian mechanism design relies on the common prior assumption,
but such prior is often not available in practice. We study the design of
prior-independent mechanisms that relax this assumption: the seller is selling
an indivisible item to buyers such that the buyers' valuations are drawn
from a joint distribution that is unknown to both the buyers and the seller;
buyers do not need to form beliefs about competitors, and the seller assumes
the distribution is adversarially chosen from a specified class. We measure
performance through the worst-case regret, or the difference between the
expected revenue achievable with perfect knowledge of buyers' valuations and
the actual mechanism revenue.
We study a broad set of classes of valuation distributions that capture a
wide spectrum of possible dependencies: independent and identically distributed
(i.i.d.) distributions, mixtures of i.i.d. distributions, affiliated and
exchangeable distributions, exchangeable distributions, and all joint
distributions. We derive in quasi closed form the minimax values and the
associated optimal mechanism. In particular, we show that the first three
classes admit the same minimax regret value, which is decreasing with the
number of competitors, while the last two have the same minimax regret equal to
that of the single buyer case. Furthermore, we show that the minimax optimal
mechanisms have a simple form across all settings: a second-price auction with
random reserve prices, which shows its robustness in prior-independent
mechanism design. En route to our results, we also develop a principled
methodology to determine the form of the optimal mechanism and worst-case
distribution via first-order conditions that should be of independent interest
in other minimax problems.Comment: An extended abstract of this work appeared in Proceedings of the 23rd
ACM Conference on Economics and Computation (EC'22
The All-Pay Auction with Complete Information
In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show that the set of equilibria is much larger than has been recognized in the literature. When there are more than two players, for instance, we show that even when the auction is symmetric there exists a continuum of asymmetric equilibria. Moreover, for economically important configurations of valuations, there is no revenue equivalence across the equilibria; asymmetric equilibria imply higher expected revenues than the symmetric equilibrium
Information and Competition in U.S. Forest Service Timber Auctions
This paper analyzes the role of private information in U.S. Forest Service timber auctions. In these auctions, firms bid a per unit price for each timber species. Total bids are computed by multiplying these prices by Forest Service volume estimates, but payments depend on actual volumes harvested. We develop an equilibrium theory for these auctions. We then relate (ex post) data about volume to (ex ante) bids. We show that bidders have private information about volumes of species and use it as predicted by theory. Differences in bidder estimates appear to affect the allocation of tracts, but competition limits information rents. We have benefited from the helpful comments of Pa
Identification and Inference in First-Price Auctions with Risk Averse Bidders and Selective Entry
We study identiļ¬cation and inference in ļ¬rst-price auctions with risk averse bidders and selective entry, building on a flexible entry and bidding framework we call the Aļ¬iliated Signal with Risk Aversion (AS-RA) model. Assuming that the econometrician observes either exogenous variation in the number of potential bidders (N) or a continuous instrument (z) shifting opportunity costs of entry, we provide a sharp characterization of the nonparametric restrictions implied by equilibrium bidding. Given variation in either competition or costs, this characterization implies that risk neutrality is nonparametrically testable in the sense that if bidders are strictly risk averse, then no risk neutral model can rationalize the data. In addition, if both instruments (discrete N and continuous z) are available, then the model primitives are nonparametrically point identiļ¬ed. We then explore inference based on these identiļ¬cation results, focusing on set inference and testing when primitives are set identiļ¬ed. Keywords: Auctions, entry, risk aversion, identiļ¬cation, set inference