Approximate Revenue from Finite Range Mechanisms

TL;DR

This paper demonstrates that in certain economic settings, the revenue from complex strategy-proof mechanisms can be approximated by simpler mechanisms with finite range, simplifying analysis and design.

Contribution

It shows that for rich single crossing domains, any strategy-proof and individually rational mechanism can be approximated by mechanisms with finite range, facilitating easier study of optimal mechanisms.

Findings

Revenue from complex mechanisms can be approximated by finite-range mechanisms.

Finite-range mechanisms are sufficient for studying optimal strategies.

Simplifies the analysis of strategy-proof mechanisms in economic environments.

Abstract

We consider an economic environment where a seller wants to sell an indivisible unit of good to a buyer. We show that revenue from any strategy-proof and individually rational mechanism defined on closed intervals of rich single crossing domains considered in \citep{Goswami1}, can be approximated by the revenue from a sequence of strategy-proof and individually rational mechanisms with finite range. Thus while studying optimal mechanisms without loss of generality we can study mechanisms with finite range.