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 supplier.s cost sometimes result in a major change...

This paper characterizes the Nash equilibrium in a pay-as-bid (discriminatory), divisible-good, procurement auction. Demand by the auctioneer is uncertain as in the supply function equilibrium model. A closed form expression is derived. Existence of an equilibrium is ensured if the hazard rate...

In multi-unit auctions, such as auctions of commodities and securities, and financial exchanges, it is necessary to specify rationing rules to break ties between multiple marginal bids. The standard approach in the literature and in practice is to ration marginal bids proportionally. This paper...