The Simplicity of Optimal Dynamic Mechanisms

TL;DR

This paper demonstrates that in dynamic markets with multiple buyers and limited supply, optimal revenue mechanisms can be implemented using simple posted prices and capacity rationing without regularity assumptions or i.i.d. conditions, especially in the continuum limit.

Contribution

It extends the understanding of optimal dynamic mechanisms by removing regularity and i.i.d. assumptions, showing that posted prices and capacity rationing suffice in the continuum limit.

Findings

Optimal mechanisms can be implemented with posted prices and capacity rationing.

The result holds without regularity or i.i.d. assumptions.

Rationing becomes unnecessary with unlimited supply.

Abstract

A fundamental economic question is that of designing revenue-maximizing mechanisms in dynamic environments. This paper considers a simple yet compelling market model to tackle this question, where forward-looking buyers arrive at the market over discrete time periods, and a monopolistic seller is endowed with a limited supply of a single good. In the case of i.i.d. and regular valuations for the buyers, Board and Skrzypacz (2016) characterized the optimal mechanism and proved the optimality of posted prices in the continuous-time limit. Our main result considers the limit case of a continuum of buyers, establishing that for arbitrary independent buyers' valuations, posted prices and capacity rationing can implement the optimal anonymous mechanism. Our result departs from the literature in three ways: It does not make any regularity assumptions, it considers the case of general, not necessarily i.i.d., arrivals, and finally, not only posted prices but also capacity rationing takes part in the optimal mechanism. Additionally, if supply is unlimited, we show that the rationing effect vanishes, and the optimal mechanism can be implemented using posted prices only, \`a la Board (2008).