Price Instability in Multi-Unit Auctions

Abstract

We consider a procurement auction, where each supplier has private costs and submits a stepped supply function. We solve for a Bayesian Nash equilibrium and show that the equilibrium has a price instability in the sense that a minor change in a suppliers cost sometimes result in a major change in the market price. In wholesale electricity markets, we predict that the bid price of the most expensive production unit can change by 1-10% due to price instability. The price instability is reduced when suppliers have more steps in their supply functions for a given production technology. In the limit, as the number of steps increases and the cost uncertainty decreases, the Bayesian equilibrium converges to a pure-strategy NE without price instability, the Supply Function Equilibrium (SFE).

Keywords: Multi-unit auctions, indivisible unit, price instability, Bayesian Nash equilibria, supply function equilibria, convergence of Nash equilibria, wholesale electricity markets

JEL Classification: C62, C72, D43, D44, L94