Two-Buyer Sequential Multiunit Auctions with No Overbidding

TL;DR

This paper analyzes equilibria in sequential multiunit auctions with two buyers, revealing a three-phase structure, the declining price anomaly, and a specific price of anarchy, under no-overbidding assumptions.

Contribution

It characterizes the equilibrium structure in sequential auctions with no-overbidding, establishing the phases, price dynamics, and efficiency bounds.

Findings

Equilibria have three phases: competitive, competition reduction, and monopsony.

Prices weakly decrease over time at equilibrium.

The price of anarchy is exactly 1 - 1/e.

Abstract

We study equilibria in two-buyer sequential second-price (or first-price) auctions for identical goods. Buyers have weakly decreasing incremental values, and we make a behavioural no-overbidding assumption: the buyers do not bid above their incremental values. Structurally, we show equilibria are intrinsically linked to a greedy bidding strategy. We then prove three results. First, any equilibrium consists of three phases: a competitive phase, a competition reduction phase and a monopsony phase. In particular, there is a time after which one buyer exhibits monopsonistic behaviours. Second, the declining price anomaly holds: prices weakly decrease over time at any equilibrium in the no-overbidding game, a fact previously known for equilibria with overbidding. Third, the price of anarchy of the sequential auction is exactly $1 - 1/e$.