This paper studies the English (progressive) auction for an exchange economy with multiple objects. The English auction is a tatonnement process and lasts multiple rounds. It is modeled as a sequence of round games. Each round game is a normal form game in which an agent's strategies are his...

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...