[Paper Review] Bidding under uncertainty: theory and experiments

Amy Greenwald, Justin A. Boyan|arXiv (Cornell University)|Jul 7, 2004

Auction Theory and Applications13 references48 citations

TL;DR

This paper investigates optimal bidding strategies in combinatorial auctions with complementary and substitutable goods across sequential, simultaneous, and hybrid (TAC Classic) auction formats. It formulates sequential bidding as an MDP, proving expected marginal utility bidding optimal, while showing marginal utility bidding suboptimal in simultaneous auctions; two approximation methods—expected-value and sampling-based—are proposed, with experiments confirming their performance in the TAC Classic setting.

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.

Motivation & Objective

• To analyze bidding strategies in combinatorial auctions where goods are complements or substitutes.
• To model sequential auction bidding as a Markov Decision Process (MDP) and identify optimal policies.
• To investigate the limitations of marginal utility bidding in simultaneous auctions and propose better approximation methods.
• To evaluate the performance of proposed bidding strategies in the TAC Classic hotel auction environment.
• To compare deterministic and stochastic approximation techniques for solving complex auction bidding problems.

Proposed method

• Formulates sequential auction bidding as a Markov Decision Process (MDP) to model dynamic decision-making under uncertainty.
• Derives expected marginal utility bidding as the optimal policy for sequential auctions using MDP framework.
• Models simultaneous auction bidding as a stochastic program to capture uncertainty in opponent behavior and valuations.
• Proposes two approximation methods: one using expected values (optimal in deterministic settings), and another using Monte Carlo sampling (asymptotically optimal).
• Employs experimental evaluation in the TAC Classic auction environment to compare the performance of different bidding policies.
• Uses the TAC Classic hybrid auction format—combining sequential and simultaneous elements—as a realistic testbed for strategy evaluation.

Experimental results

Research questions

• RQ1 Is expected marginal utility bidding the optimal strategy in sequential combinatorial auctions with complementary and substitutable goods?
• RQ2 Does marginal utility bidding remain optimal in simultaneous combinatorial auctions, even under deterministic conditions?
• RQ3 Can stochastic programming approximation methods improve bidding performance in simultaneous auctions compared to marginal utility bidding?
• RQ4 How do expected-value and sampling-based approximation methods compare in solving the stochastic program for simultaneous auctions?
• RQ5 How do the proposed bidding strategies perform in a realistic, hybrid auction environment like TAC Classic?

Key findings

• Expected marginal utility bidding is proven to be the optimal policy in sequential auctions, as formulated by the MDP model.
• Marginal utility bidding is not optimal in simultaneous auctions, even in deterministic settings, as demonstrated by counterexample.
• The expected-value approximation method is optimal in deterministic environments, providing a solid baseline for known distributions.
• The sampling-based method is asymptotically optimal as the number of samples increases, offering a robust approach for stochastic settings.
• Experimental results in the TAC Classic environment show that the sampling-based method outperforms marginal utility bidding in terms of expected utility and final payoff.
• The hybrid TAC Classic setting reveals that strategy performance depends heavily on the auction format’s mix of sequential and simultaneous elements.