Auctions are becoming an increasingly popular method for transacting business, especially over the Internet. This article presents a general approach to building autonomous bidding agents to bid in multiple simultaneous auctions for interacting goods. A core component of our approach learns a model of the empirical price dynamics based on past data and uses the model to analytically calculate, to the greatest extent possible, optimal bids. We introduce a new and general boosting-based algorithm for conditional density estimation problems of this kind, i.e., supervised learning problems in which the goal is to estimate the entire conditional distribution of the real-valued label. This approach is fully implemented as ATTac-2001, a top-scoring agent in the second Trading Agent Competition (TAC-01). We present experiments demonstrating the effectiveness of our boosting-based price predictor relative to several reasonable alternatives.

Given a knowledge base KB containing first-order and statistical facts, we consider a principled method, called the random-worlds method, for computing a degree of belief that some formula Phi holds given KB. If we are reasoning about a world or system consisting of N individuals, then we can consider all possible worlds, or first-order models, withdomain {1,...,N} that satisfy KB, and compute thefraction of them in which Phi is true. We define the degree of belief to be the asymptotic value of this fraction as N grows large. We show that when the vocabulary underlying Phi andKB uses constants and unary predicates only, we can naturally associate an entropy with each world. As N grows larger,there are many more worlds with higher entropy. Therefore, we can usea maximum-entropy computation to compute the degree of belief. This result is in a similar spirit to previous work in physics and artificial intelligence, but is far more general. Of equal interest to the result itself are the limitations on its scope. Most importantly, the restriction to unary predicates seems necessary. Although the random-worlds method makes sense in general, the connection to maximum entropy seems to disappear in the non-unary case. These observations suggest unexpected limitations to the applicability of maximum-entropy methods.