Mechanism Design via Market Clearing-Prices for Value Maximizers under Budget and RoS Constraints
Xiaodong Liu, Weiran Shen, Zihe Wang
TL;DR
A market-clearing mechanism is designed and proved to be incentive-compatible with respect to financial constraints, making truthful reporting the optimal strategy, and it achieves a tight 1/2-approximation of the first-best revenue benchmark, the maximum revenue of any feasible mechanism, regardless of IC.
Abstract
The transition to auto-bidding in online advertising has shifted the focus of auction theory from quasi-linear utility maximization to value maximization subject to financial constraints. We study mechanism design for buyers with private budgets and private Return-on-Spend (RoS) constraints, but public valuations, a setting motivated by modern advertising platforms where valuations are predicted via machine learning models. We introduce the extended Eisenberg-Gale program, a convex optimization framework generalized to incorporate RoS constraints. We demonstrate that the solution to this program is unique and characterizes the market's competitive equilibrium. Based on this theoretical analysis, we design a market-clearing mechanism and prove two key properties: (1) it is incentive-compatible with respect to financial constraints, making truthful reporting the optimal strategy; and (2) it achieves a tight 1/2-approximation of the first-best revenue benchmark, the maximum revenue of any feasible mechanism, regardless of IC. Finally, to enable practical implementation, we present a decentralized online algorithm. Ignoring logarithmic factors, we prove that under this algorithm, both the seller's revenue and each buyer's utility converge to the equilibrium benchmarks with a sublinear regret of $\tilde{O}(\sqrt{m})$ over $m$ auctions.