A First-Price Sealed-Bid Asymmetric Auction When Two Bidders Have Respective CRRA and General Utility Functions

We study a first-price auction with two bidders where one bidder is characterized by a constant relative risk aversion utility function (i.e., a concave power function) while the other has a general concave utility function. We establish the existence and uniqueness of the optimal strategic markups and analyze the effects of one bidder’s risk aversion level on the optimal strategic markups of him and his opponent’s, the allocative efficiency of the auction, and the seller’s expected revenue, respectively.

How Accurately Do Structural Asymmetric First-Price Auction Estimates Represent True Valuations?

Structural asymmetric first-price auction estimation methods have provided numerous empirical studies. However, due to the latent nature of underlying valuations, the accuracy of estimates is not feasibly testable with field data, a fact that could inhibit empirical auction market designs and applications based on structural estimates. To assess their accuracy, we provide an analysis of estimates derived from experimental asymmetric auction data, in which researchers observe valuations. We test the null of statistical equivalence between the estimated and true value distributions against the alternative of non-equivalence. When advanced models are used, the Modified Kolmogorov-Smirnov test fails to reject the distributional equivalence, supporting structural asymmetric auction estimations for auction market studies. In addition, recovered efficiencies have plus-minus 2.5 percent precision, compared to the true efficiencies.

Revenue Comparison in Asymmetric Auctions with Discrete Valuations

We consider an asymmetric auction setting with two bidders such that the valuation of each bidder has a binary support. First, we characterize the unique equilibrium outcome in the first price auction for any values of parameters. Then we compare the first price auction with the second price auction in terms of expected revenue. Under the assumption that the probabilities of low values are the same for the two bidders, we obtain two main results: (i) the second price auction yields a higher revenue unless the distribution of a bidder’s valuation first-order stochastically dominates the distribution of the other bidder’s valuation “in a strong sense” and (ii) introducing reserve prices implies that the first price auction is never superior to the second price auction. In addition, in some cases, the revenue in the first price auction decreases when all the valuations increase.

Millers, Commission Agents and Collusion in Grain Markets: Evidence from Basmati Auctions in North India

This paper undertakes structural estimation of asymmetric auction models in a market for basmati, and detects the presence of a cartel consisting of a large (in market share) local miller and commission agents purchasing for large distant millers. The contracts between the distant millers and their commission agents help to explain the specific form that collusion takes. Simulations indicate that (i) the cartel gains considerably by colluding, over the competitive outcome; (ii) however, sellers (farmers) do not lose significantly under collusion when the commission agents bid. The paper also shows that efficient collusion, the form of collusion commonly assumed in the literature, does not explain the data well.