Bidding in Uniform Price Auctions for Value Maximizing Buyers

2024-06-06

arXiv.org

AI Summary

This paper studies robust bidding strategies for value-maximizing buyers in repeated uniform-price multi-unit auctions, aiming to maximize cumulative value over $T$ rounds while satisfying a return-on-investment (RoI) constraint in each round. We propose the $m$-uniform bid format—submitting $m$ price-quantity pairs—and introduce the Universal Feasibility (UF) strategy class, formally defined and proven equivalent to generalized truthful bidding under RoI constraints. Our theoretical contributions are: (1) defining the Price of Universal Feasibility (PoUF), proving $ ext{PoUF} leq 2$ with tightness; and (2) establishing that $m$-uniform bidding yields at most an $m$-fold value gain over single-uniform bidding. Game-theoretic modeling and semi-synthetic simulations demonstrate that UF strategies strictly satisfy RoI under arbitrary bidder behavior, significantly outperform theoretical bounds in practice, and exhibit both strong robustness and practical applicability.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the problem of bidding in uniform price auctions widely used in practice. Although these auctions are non-truthful for bidders with quasilinear utility functions, several empirical findings suggest that the auction format induces truthful bidding from the bidders. We attribute this difference in theory and practice to the assumption of the behavioral model of the bidders. In this pursuit, we study uniform price auctions in a repeated setting from the perspective of a value-maximizing buyer who aims to maximize their acquired cumulative value across $T$ rounds, subject to per-round return-on-investment (RoI) constraints. For a RoI-constrained, value-maximizing buyer, we study a generalized version of the uniform bidding format, commonly used in practice, which we term as $m$-uniform bidding. To characterize the optimal $m$-uniform bid, we introduce and study the notion of universally feasible (UF) bidding policies, which are robust, meaning that RoI feasibility is obtained regardless of the competitors' bids. We show that the optimal class of UF bidding policies is essentially a generalization of truthful bidding policies, which depends only on the valuation curve of the bidder and target RoI. To measure the performance of UF bidding policies against the optimal bidding policy that is not necessarily UF, we introduce a metric called the Price of Universal Feasibility (PoUF) and establish that PoUF is at most 2, irrespective of $m$ and the upper bound is tight. We further compare the generalized $m$-uniform bidding interface against the classical uniform bidding format under which $m=1$, showing the total value under $m$-uniform bidding increases at most by a factor of $m$. Numerical simulations on semi-synthetic data demonstrate that UF bidding policies perform significantly better than the derived theoretical bounds.

Problem

• Maximize buyer's cumulative value in uniform price auctions
• Ensure return-on-investment constraints are met each round
• Learn optimal safe bidding strategies with sublinear regret

Innovation

• Safe bidding strategies for RoI constraints
• Polynomial-time optimal safe strategy algorithm
• α-approximate sublinear regret performance