Efficiency of Non-Truthful Auctions in Auto-bidding with Budget Constraints
Christopher Liaw, Aranyak Mehta, Wennan Zhu

TL;DR
This paper analyzes the efficiency of non-truthful auction mechanisms for auto-bidders with budget constraints, demonstrating the optimality of first-price auctions and the benefits of randomization under various assumptions.
Contribution
It establishes the optimality of deterministic first-price auctions and demonstrates how randomization improves efficiency bounds in budget-constrained auto-bidding.
Findings
First-price auction (FPA) has a tight PoA of n without assumptions.
Under a budget-value assumption, PoA of FPA improves to 2.
Randomized mechanisms like rFPA achieve PoA below 2, outperforming deterministic mechanisms.
Abstract
We study the efficiency of non-truthful auctions for auto-bidders with both return on spend (ROS) and budget constraints. The efficiency of a mechanism is measured by the price of anarchy (PoA), which is the worst case ratio between the liquid welfare of any equilibrium and the optimal (possibly randomized) allocation. Our first main result is that the first-price auction (FPA) is optimal, among deterministic mechanisms, in this setting. Without any assumptions, the PoA of FPA is which we prove is tight for any deterministic mechanism. However, under a mild assumption that a bidder's value for any query does not exceed their total budget, we show that the PoA is at most . This bound is also tight as it matches the optimal PoA without a budget constraint. We next analyze two randomized mechanisms: randomized FPA (rFPA) and "quasi-proportional" FPA. We prove two results that…
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Taxonomy
TopicsAuction Theory and Applications · Experimental Behavioral Economics Studies · Consumer Market Behavior and Pricing
