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...

The third generation UMTS auction in Germany raised an enormous amount of revenue, and at the same time achieved a more competitive market structure than other UMTS auctions in Europe. The present paper explains the design of that auction, and presents a game theoretic explanation of observed...

The third generation UMTS auction in Germany raised an enormous amount of revenue, and at the same time achieved a more competitive market structure than other UMTS auctions in Europe. The present paper explains the design of that auction, and presents a game theoretic explanation of observed...

We analyse how the market design influences the bidding behaviour in multi-unit auctions, such as wholesale electricity markets. It is shown that competition improves for increased market transparency and we identify circumstances where the auctioneer prefers uniform to discriminatory pricing....

The literature on aggregative games, which has been applied in the study of contests, has focused on simultaneous games. We apply aggregative games techniques in a novel fashion in the analysis of sequential lottery contests with n players. It is shown that: (1) there exists a unique subgame...

This article describes a large number of contestants with high and low talent who individually decide to enter a contest or take their heterogeneous outside options. We derive a critical condition for which only high types, only low types, or both types participate in the contest. If a contest...