Non-Quasi-Linear Agents in Quasi-Linear Mechanisms (Extended Abstract)

Authors Moshe Babaioff, Richard Cole, Jason Hartline, Nicole Immorlica, Brendan Lucier

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Author Details

Moshe Babaioff
  • Microsoft Research, Herzliya, Israel
Richard Cole
  • New York University, New York City, NY, USA
Jason Hartline
  • Northwestern University, Evanston, IL, USA
Nicole Immorlica
  • Microsoft Research, Cambridge, MA, USA
Brendan Lucier
  • Microsoft Research, Cambridge, MA, USA

Cite AsGet BibTex

Moshe Babaioff, Richard Cole, Jason Hartline, Nicole Immorlica, and Brendan Lucier. Non-Quasi-Linear Agents in Quasi-Linear Mechanisms (Extended Abstract). In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, p. 84:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quality of equilibria
  • Return on investment
  • Non-quasi-linear agents
  • Transferable Welfare
  • Simultaneous Second-Price Auctions


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