Using the concept of market-distribution functions, we derive general optimality conditions for discriminatory divisible-good auctions, which are also applicable to Bertrand games and non-linear pricing. We introduce the concept of offer distribution function to analyze randomized offer curves,...

Using the concept of market-distribution functions, we derive general optimality conditions for discriminatory divisible-good auctions, which are also applicable to Bertrand games and non-linear pricing. We introduce the concept of o¤er distribution function to analyze randomized offer curves,...

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...

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...

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...