This award funds research using computational methods on a problem in mechanism design that is especially important in understanding the likely outcomes of complicated auctions.
The research team use mechanism design theory and linear programming techniques to consider whether first-price auctions are more or less vulnerable to collusion than second-price or ascending bid auctions. They also determine how a tacit or explicit cartel might operate in a variety of different kinds of auctions.
The research has substantial broader impacts because auction methods are widly used. The Federal government currently uses auctions to allocate telecommunications spectrum and rights to offshore drilling, timber, and mining. Proposals to use a 'cap and trade' system to reduce greenhouse gas emissions also rely on auction methods.
The project has produced the following published and forthcoming papers: 1. Sandro Brusco, Giuseppe Lopomo, and Leslie M. Marx, "The 'Google Effect' in the FCC's 700 MHz Auction," Information Economics and Policy 21, 101-114 (2009). We describe and interpret bidding behavior in FCC Auction 73 for the C-block licenses. These licenses were initially offered subject to an open platform restriction, which was highly valued by firms such as Google. Google entered bids until its bids reached the C-block reserve price, thereby ensuring that the open platform restriction would be applied to the licenses. Later in the auction, other bidders outbid Google, so Google was able to trigger the open platform restriction without having to purchase any of the licenses. Aiming at providing a formal analysis of actual bidding behavior in this auction, we develop a formal game-theoretic model that allows for bidders such as Google. After presenting a detailed description of how the bidding in the C-block progressed during the auction, we use our model as a guide for understanding the observed bidding behavior in the C block. The analysis of the model together with an examination of the bid data allows us to make some suggestions for how future auctions might be improved. 2. Alexandre Belloni, Giuseppe Lopomo, and Shouqiang Wang, "Multi-dimensional Mechanism Design: Finite Dimensional Approximations and Efficient Computation," forthcoming in Operations Research. Multidimensional mechanism design problems have proven difficult to solve by extending techniques from the one-dimensional case. This paper considers mechanism design problems with multidimensional types when the seller's cost function is not separable across buyers. We show that an associated in finite-dimensional optimization problem posed by the theoretical model can be approximated arbitrary well by a sequence of finite-dimensional linear programming problems. We provide an efficient, i.e. terminating in polynomial time in the problem size, method to compute the separation oracle associated with the Border constraints and incentive compatibility constraints. This implies that our finite-dimensional approximation is solvable in polynomial time. Finally, we illustrate how the numerical solutions of the finite-dimensional approximations can provide insights into the nature of optimal solutions to the in finite-dimensional problem in particular cases. 3.Giuseppe Lopomo, Leslie M. Marx, and Peng Sun, "Bidder Collusion at First-Price Auctions," forthcoming in Review of Economic Design. We show that in simple environments, a bidding ring operating at a first-price sealed-bid auctions cannot achieve any gains relative to non-cooperative bidding if the ring is unable to control the bids that its members submit at the auction. This contrasts with results for the case in which the ring can control its members' bids or prevent all but one of the ring members from participating in the auction. Numerical results suggest that this result extends to some more complex environments. Thus, this research supports the recommendation that sellers concerned about bidder collusion should use a first-price auction format. The analytic results use linear programming techniques that have potential applications to a number of other economic problems. 4.Sandro Brusco, Giuseppe Lopomo, and Leslie M. Marx, "The Economics of Contingent Re-Auctions," American Economic Journal: Microeconomics, 3(2), 165-193, (2011). We consider an auction environment where an object can be sold with usage restrictions that generate benefits to the seller but decrease buyers' valuations. In this environment, sellers such as the FCC have used "contingent re-auctions," offering the restricted object with a reserve price, but re-auctioning it without restrictions if the reserve is not met. We show that contingent re-auctions are generally neither efficient nor optimal for the seller. We propose an alternative "exclusive-buyer mechanism" that can implement the efficient outcome in dominant strategies. In certain environments, parameters can be chosen so the seller's surplus is maximized across all selling procedures. 5.Giuseppe Lopomo, Leslie M. Marx, David McAdams, and Brian Murray, "Carbon Allowance Auction Design: An Assessment of Options for the U.S.," forthcoming in Review of Environmental Economics and Policy. Carbon allowance auctions are a component of existing and proposed regional cap-and-trade programs in the U.S. and are also included in recent bills in the U.S. Congress that would establish a national cap-and-trade program to regulate greenhouse gases. We discuss and evaluate the two leading candidates for auction format: a uniform-price sealed-bid auction and an ascending-bid dynamic auction. We identify the primary trade-offs between these two formats as applied to carbon allowance auctions and suggest additional auction design features that address potential concerns about efficiency losses from collusion and other factors. We conclude that, based on currently available evidence, a uniform-price sealed-bid auction is more appropriate for the sale of carbon allowances than the other leading auction formats, in part because it offers increased robustness to collusion without significant sacrifice of price discovery.
