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Unformatted text preview: Bidding under Uncertainty: Theory and Experiments Amy Greenwald Department of Computer Science Brown University, Box 1910 Providence, RI 02912 email@example.com Justin Boyan ITA Software 141 Portland Street Cambridge, MA 02139 firstname.lastname@example.org Abstract This paper describes a study of agent bid- ding strategies, assuming combinatorial val- uations for complementary and substitutable goods, in three auction environments: se- quential auctions, simultaneous auctions, and the Trading Agent Competition (TAC) Clas- sic hotel auction design, a hybrid of sequen- tial and simultaneous auctions. The prob- lem of bidding in sequential auctions is for- mulated as an MDP, and it is argued that expected marginal utility bidding is the opti- mal bidding policy. The problem of bidding in simultaneous auctions is formulated as a stochastic program, and it is shown by ex- ample that marginal utility bidding is not an optimal bidding policy, even in determinis- tic settings. Two alternative methods of ap- proximating a solution to this stochastic pro- gram are presented: the first method, which relies on expected values, is optimal in deter- ministic environments; the second method, which samples the nondeterministic environ- ment, is asymptotically optimal as the num- ber of samples tends to infinity. Finally, ex- periments with these various bidding policies are described in the TAC Classic setting. 1 Introduction One of the key challenges autonomous bidding agents face is to determine how to bid on complementary and substitutable goodsi.e., goods with combinatorial valuationsin auction environments. Complemen- tary goods are goods with superadditive valuations: v ( A B ) + v ( AB ) v ( AB ); substitutable goods are goods with subadditive valuations: v ( A B ) + v ( AB ) v ( AB ). In general, it is impossible to assign indepen- dent valuations to complementary goods, which can be worthless in isolation, or to substitutable goods, which can be worthwhile only in isolation. Thus, the simple bidding strategy for each good x , bid its valuation is inapplicable in this framework. This paper investi- gates a class of bidding strategies for various auction environments, assuming combinatorial valuations for complementary and substitutable goods. Specifically, we consider three auction environments: sequential auctions, simultaneous auctions, and the hybrid of sequential and simultaneous auctions imple- mented in TAC Classic. 1 As the name suggests, in se- quential auctions, goods are sold sequentially, in some fixed, known order. Here, agents can reason about each good in turn, basing future decisions on past out- comes. But in simultaneous auctions all goods are sold simultaneously. Here, agents must reason about all goods simultaneously, with only one opportunity to make one bidding decision that pertains to all goods....
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- Fall '08
- Computer Science