# Non-quasi-linear Agents in Quasi-linear Mechanisms

arXiv: https://arxiv.org/abs/2012.02893 · HTML: https://mlsanity.com/paper/2012.02893/

## Key facts

- Cited by 6 papers in the map (data through 13 Oct 2026).
- First posted on arXiv 4 Dec 2020.

## Built on by (most cited first, 6 of 6)

- [Autobidders with Budget and ROI Constraints: Efficiency, Regret, and Pacing Dynamics](https://mlsanity.com/paper/2301.13306/) (2023)
- [Online Bidding Algorithms for Return-on-Spend Constrained Advertisers](https://mlsanity.com/paper/2208.13713/) (2022)
- [Online Learning under Budget and ROI Constraints via Weak Adaptivity](https://mlsanity.com/paper/2302.01203/) (2023)
- [Optimal Spend Rate Estimation and Pacing for Ad Campaigns with Budgets](https://mlsanity.com/paper/2202.05881/) (2022)
- [Autobidding Arena: unified evaluation of the classical and RL-based autobidding algorithms](https://mlsanity.com/paper/2510.19357/) (2025)
- [Online Bidding Algorithms with Strict Return on Spend (ROS) Constraint](https://mlsanity.com/paper/2502.05599/) (2025)

## Abstract (arXiv)

Mechanisms with money are commonly designed under the assumption that agents are quasi-linear, meaning they have linear disutility for spending money. We study the implications when agents with non-linear (specifically, convex) disutility for payments participate in mechanisms designed for quasi-linear agents. We first show that any mechanism that is truthful for quasi-linear buyers has a simple best response function for buyers with non-linear disutility from payments, in which each bidder simply scales down her value for each potential outcome by a fixed factor, equal to her target return on investment (ROI). We call such a strategy ROI-optimal. We prove the existence of a Nash equilibrium in which agents use ROI-optimal strategies for a general class of allocation problems. Motivated by online marketplaces, we then focus on simultaneous second-price auctions for additive bidders and show that all ROI-optimal equilibria in this setting achieve constant-factor approximations to suitable welfare and revenue benchmarks.