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arXiv · 2504.14948

Mechanism Design for Auctions with Externalities on Budgets

Yusen Zheng·Yukun Cheng·Chenyang Xu·Xiaotie Deng
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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.

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BibTeXRIS

Yusen Zheng, Yukun Cheng, Chenyang Xu, Xiaotie Deng. 2025-04-21. Mechanism Design for Auctions with Externalities on Budgets. https://arxiv.org/abs/2504.14948

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