Simple Mechanisms for Agents with Non-linear Utilities

TL;DR

This paper demonstrates that economic mechanisms effective for linear utility agents can be approximately applied to non-linear utility agents, including those with risk aversion, budget constraints, and endogenous valuations, by quantifying their similarities.

Contribution

It extends linear utility mechanism results to non-linear utility models by providing bounds and showing simple mechanisms remain approximately optimal.

Findings

Non-linear utility agents can be approximated by linear utility models within quantifiable bounds.

Simple mechanisms are approximately optimal for non-linear utility agents.

The framework applies to revenue and welfare objectives in various non-linear models.

Abstract

We show that economic conclusions derived from Bulow and Roberts (1989) for linear utility models approximately extend to non-linear utility models. Specifically, we quantify the extent to which agents with non-linear utilities resemble agents with linear utilities, and we show that the approximation of mechanisms for agents with linear utilities approximately extend for agents with non-linear utilities. We illustrate the framework for the objectives of revenue and welfare on non-linear models that include agents with budget constraints, agents with risk aversion, and agents with endogenous valuations. We derive bounds on how much these models resemble the linear utility model and combine these bounds with well-studied approximation results for linear utility models. We conclude that simple mechanisms are approximately optimal for these non-linear agent models.