Robust Temporal Guarantees in Budgeted Sequential Auctions

2026-02-20

AI Summary

This work addresses the vulnerability of existing no-regret learning algorithms in budget-constrained sequential auctions, which are susceptible to strategic manipulation and lack dynamic performance guarantees. The authors propose a novel algorithm grounded in deterministic learning strategies and adversarial analysis, achieving strong proportional guarantees on the number of wins over arbitrary time intervals while respecting budget conservation constraints—thereby transcending the limitations of traditional no-regret frameworks. Theoretically, a single agent employing this algorithm is guaranteed to win at least ρT − O(√T) rounds. Moreover, when all agents adopt the proposed strategy, the deviation from proportional fairness in any interval of length O(√T) becomes bounded by a constant after only O(√T log T) rounds.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In modern advertising platforms, learning algorithms are deployed by budget-constrained bidders to maximize their accumulated value. These algorithms often offer classical utility guarantees like no-regret, i.e., the agent's utility is at least the utility achieved by some benchmark in which it is assumed that every other agent's bidding remains the same. These guarantees offer compelling properties: They are optimal against stationary competition distributions, and in unconstrained settings, the resulting empirical distribution of play induced by no-regret dynamics approximates a Coarse Correlated Equilibrium. However, no-regret algorithms are easily manipulable, and in budgeted settings, no stronger notion of regret (such as swap regret) is currently known that would limit such manipulation. We propose a very simple learning algorithm for budgeted sequential auctions where agents maximize their total number of wins and show that it has surprisingly appealing properties. We analyze this algorithm from two perspectives. First, we show that when an agent with a $\rho$ fraction of the total budget uses this algorithm, then she is guaranteed to win at least $\rho T - O(\sqrt T)$ of the total $T$ rounds. This result holds for adversarial behavior by the other agents, as long as they respect their own budget restrictions. Second, we examine the scenario when all the agents follow our algorithm. By the first result, every agent's total wins are proportional to her budget, up to the additive $O(\sqrt T)$ term. In addition, we show that this result holds in a much stronger sense: after an initial period of $O(\sqrt T \log T)$ rounds, every agent gets the same guarantee over any time interval. For intervals of length $O(\sqrt T)$, we show that the deviation from the desired number of wins is an additive constant.

Problem

• budgeted sequential auctions
• no-regret learning
• strategic manipulation
• temporal guarantees
• adversarial bidding

Innovation

• budgeted sequential auctions
• temporal fairness
• adversarial robustness
• proportional wins
• online learning