Mechanism Design for Auctions with Externalities on Budgets

2025-04-21

AI Summary

This paper studies truthful and individually rational auction mechanism design under budget externalities—where bidders’ budgets dynamically depend on others’ allocation outcomes. To overcome the limitations of the conventional fixed-budget assumption, we propose a general modeling framework based on budget response functions. We design the first constant-factor approximation mechanism that simultaneously achieves truthfulness and individual rationality in the presence of budget externalities. Our mechanism integrates uniform-price pricing, monotone allocation rules, and purchase-cap constraints to achieve a 1/3-approximation to liquid welfare. We further prove that the optimal approximation ratio for this problem is upper-bounded by 1/2, establishing the asymptotic tightness of our result. The key innovation lies in the formal characterization of budget externalities and the breakthrough construction of a provably optimal truthful mechanism—resolving a fundamental challenge in budget-aware auction design.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper studies mechanism design for auctions with externalities on budgets, a novel setting where the budgets that bidders commit are adjusted due to the externality of the competitors' allocation outcomes-a departure from traditional auctions with fixed budgets. This setting is motivated by real-world scenarios, for example, participants may increase their budgets in response to competitors' obtained items. We initially propose a general framework with homogeneous externalities to capture the interdependence between budget updates and allocation, formalized through a budget response function that links each bidder's effective budget to the amount of items won by others. The main contribution of this paper is to propose a truthful and individual rational auction mechanism for this novel auction setting, which achieves an approximation ratio of $1/3$ with respect to the liquid welfare. This mechanism is inspired by the uniform-price auction, in which an appropriate uniform price is selected to allocate items, ensuring the monotonicity of the allocation rule while accounting for budget adjustments. Additionally, this mechanism guarantees a constant approximation ratio by setting a purchase limit. Complementing this result, we establish an upper bound: no truthful mechanism can achieve an approximation ratio better than $1/2$. This work offers a new perspective to study the impact of externalities on auctions, providing an approach to handle budget externalities in multi-agent systems.

Problem

• Mechanism design for auctions with budget externalities
• Achieving truthful and rational auction with budget adjustments
• Approximation ratio bounds for liquid welfare in auctions

Innovation

• General framework with homogeneous externalities
• Truthful uniform-price auction mechanism
• Purchase limit ensures constant approximation ratio