Uniform price auction with quantity constraints

TL;DR

This paper analyzes uniform price auctions with asymmetric bidders and quantity constraints, presenting a method to find equilibria and showing conditions for low-price equilibria.

Contribution

It introduces an iterative procedure to identify equilibrium outcomes and ascending auctions in auctions with quantity constraints and asymmetric bidders.

Findings

Demand reduction and low-price equilibria can occur due to strategic demand withholding.

A unique low-price equilibrium exists when no bidder's quantity constraint covers the entire supply.

The paper provides a systematic way to find equilibrium outcomes in such auction settings.

Abstract

We study the equilibria of uniform price auctions where many asymmetric bidders have flat demands up to their respective quantity constraints. We present an iterative procedure that systematically finds an equilibrium outcome as well as an ascending auction that has this outcome as a dominant strategy equilibrium outcome. Demand reduction and low price equilibrium may occur since it is advantageous for a bidder to give up some of his/her demand and get the remaining demand at a low price rather than to get his/her entire demand at a higher price. We show that a low price equilibrium is the only possible equilibrium when no bidder's quantity constraint is large enough to cover the supply.