Non-quasi-linear Agents in Quasi-linear Mechanisms

TL;DR

This paper explores how mechanisms designed for quasi-linear agents perform when participants have convex, non-linear disutility for payments, revealing simple best response strategies and equilibrium properties.

Contribution

It introduces the concept of ROI-optimal strategies for non-linear disutility agents and proves equilibrium existence and approximation guarantees in auction settings.

Findings

ROI-optimal strategies are simple and scale down values by a fixed factor.

Existence of Nash equilibrium with ROI-optimal strategies in general allocation problems.

ROI-optimal equilibria in second-price auctions approximate welfare and revenue benchmarks.

Abstract

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.