Bidding under Uncertainty: Theory and Experiments

TL;DR

This paper investigates agent bidding strategies in different auction formats with combinatorial valuations, proposing optimal and approximate policies, and evaluates their performance through experiments in the TAC Classic hotel auction environment.

Contribution

It introduces a formal framework for bidding in sequential and simultaneous auctions, and compares optimal and approximate policies through experimental analysis.

Findings

Expected marginal utility bidding is optimal in sequential auctions.

Marginal utility bidding is not optimal in simultaneous auctions.

Sampling-based approximation methods perform well in stochastic environments.

Abstract

This paper describes a study of agent bidding strategies, assuming combinatorial valuations for complementary and substitutable goods, in three auction environments: sequential auctions, simultaneous auctions, and the Trading Agent Competition (TAC) Classic hotel auction design, a hybrid of sequential and simultaneous auctions. The problem of bidding in sequential auctions is formulated as an MDP, and it is argued that expected marginal utility bidding is the optimal bidding policy. The problem of bidding in simultaneous auctions is formulated as a stochastic program, and it is shown by example that marginal utility bidding is not an optimal bidding policy, even in deterministic settings. Two alternative methods of approximating a solution to this stochastic program are presented: the first method, which relies on expected values, is optimal in deterministic environments; the second method, which samples the nondeterministic environment, is asymptotically optimal as the number of samples tends to infinity. Finally, experiments with these various bidding policies are described in the TAC Classic setting.