Solving Complex Common Value Auctions Using Genetic Algorithms

Raymond Board and Michael B. Gordy
Board of Governors of the Federal Reserve System, Washington
MGordy@frb.gov

Abstract

Many of the auctions of greatest empirical interest are also those most difficult to model. Common value (CV) auctions, in which the value of the good for sale is common to the bidders but unknown to them at the time of the auction, tend especially to fall into this category. Examples include auctions of treasury bills and of oil-drilling rights. Theoretical analysis of CV auctions has been mainly limited to the prototypical case studied by Milgrom and Weber (1982), in which a single object is auctioned to a fixed group of n bidders with symmetric preferences and private information. This relatively simple model has yielded fundamental insight into the bidders' decision problem, but we often are interested in the effect of some environmental or institutional feature not captured, e.g., endogeneity in the number of bidders participating or a hidden reservation price. Generalization of the Milgrom and Weber solution appears, however, often to be analytically intractable, even to the degree that direct numerical methods are infeasible.

In this paper, we show that genetic algorithms (GA) offer one way around this apparent dead end. In contrast to direct methods, which require the solution of differential equations derived from substitution of equilibrium conditions into first order conditions from bidders' utility maximization, the GA requires only that we specify the bidders' utility functions, distributions for unobserved random variables, and a rule for choosing winning bids and payments to the seller. At some cost in elegance and computational efficiency, we gain flexibility. Adding a new feature to the auction does not add much complexity to the GA, even if it fundamentally alters the bidders' decision problem.

We apply the GA to study the effects of asymmetry in the quality of private information. It is often the case in CV auctions that some bidders are known to have more precise information than others on the value of the object. For example, in US Treasury auctions, ordinary bidders compete against primary dealers. In auctions of oil-drilling rights, a bidder who owns an adjacent tract may know more about the value of the tract for sale than other bidders. Asymmetry may also result when individual bidders compete against a collusive syndicate. Using the GA to find equilibrium bidding strategies, we show how asymmetry changes the behavior of both the better and less informed bidders. We explore how these changes affect the seller's optimal choice of auction format.