Risk-Averse Auction Agents Yaxin Liu College of Computing Georgia Tech Atlanta, GA 30332-0280 yxliu@cc.gatech.edu Richard Goodwin IBM T.J. Watson P.O. Box 218, Route 134 Yorktown Heights, NY 10598 rgoodwin@us.ibm.com Sven Koenig College of Computing Georgia Tech Atlanta, GA 30332-0280 skoenig@cc.gatech.edu ABSTRACT Auctions are an important means for purchasing material in the era of e-commerce. Research on auctions often studies them in isolation. In practice, however, auction agents are part of com- plete supply-chain management systems and have to make the same decisions as their human counterparts. To address this is- sue, we generalize results from auction theory in three ways. First, auction theory provides the optimal bidding function for the case where auction agents want to maximize the expected profit. Since companies are often risk-averse, we derive a closed form of the optimal bidding function for auction agents that maximize the expected utility of the profit for concave exponential utility func- tions. Second, auction theory often assumes that auction agents know the bidder’s valuation of an auctioned item. However, the valuation depends on how the item can be used in the production process. We therefore develop theoretical results that enable us to integrate our auction agents into production-planning systems to derive the bidder’s valuation automatically. Third, auction theory often assumes that the probability distribution over the competitors’ valuations of the auctioned item is known. We use simulations of the combined auction- and production-planning system to obtain crude approximations of these probability dis- tributions automatically. The resulting auction agents are part of a complete supply-chain management system and seamlessly combine ideas from auction theory, utility theory, and dynamic programming. Categories and Subject Descriptors I.2.8 [Computing Methodologies]: Artificial Intelli- gence—Problem Solving, Control Methods, and Search General Terms Algorithms, Economics Keywords Auctions, E-Commerce, Supply-Chain Management, Risk Aversion Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. AAMAS’03, July 14–18, 2003, Melbourne, Australia. Copyright 2003 ACM 1-58113-683-8/03/0007 ...$5.00. 1. INTRODUCTION Our goal is to develop agents that are able to make deci- sions for far more realistic planning objectives than is cur- rently possible. We do this in the context of auction plan- ning. Auctions are an important means for purchasing ma- terial in the era of e-commerce. Consequently, agents that automate or support human decision making need to be able to decide whether to participate in auctions and how much to bid. If the auction is won, a company might be able to save money compared to producing the material in house. If the auction is lost, however, the company might incur large penalties for not being able to deliver orders on time. Com- panies are therefore often risk-averse (conservative) when making these decisions and bid high to increase the chance of winning the auction. In this paper, we investigate how to build auction agents for high-stake single-instance deci- sion situations like these. High-stake decision situations are situations in which large wins or losses are possible. Single- instance decision situations are situations that are faced only once. People typically do not maximize the expected profit in high-stake single-instance decision situations. Consider, for example, that you can participate once in one (and only one) of the following two lotteries without any cost to you: Expected Expected Choices Probability Profit Profit Utility Utility Choice 1 50 percent $10,000,000 $5,000,000 0.95 0.475 50 percent $0 0.00 Choice 2 100 percent $4,500,000 $4,500,000 0.74 0.740 When people have to decide whether they would like to get 4,500,000 dollars for sure (Choice 2) or get 10,000,000 dollars with fifty percent probability and nothing otherwise (Choice 1), many people prefer Choice 2 although its ex- pected profit is clearly lower. They are risk-averse, that is, willing to accept a decrease in the expected profit to reduce the variance and thus the possibility of only a small profit. The recommendations of agents should reflect the risk aver- sion of people correctly. After all, agents make suggestions for how to act and should make the same suggestions that people would have made themselves, otherwise the agents would not be very helpful. Utility theory [4, 16] explains why people often do not maximize the expected profit in high-stake single-instance decision situations. Utility theory suggests that they max- imize expected utility, where the utility is a strictly mono- tonically increasing function of the profit. Nonlinear utility functions are necessary to model risk-averse people. Ex- periments show that utility functions in practice are of- ten approximately logarithmic. We, however, use concave exponential utility function because of their advantageous