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 most wholesale electricity markets generators must submit step-function offers of supply to a uniform price auction, and the market is cleared at the price of the most expensive offer needed to meet realised demand. Such markets can most elegantly be modelled as the pure-strategy, Nash...

The supply function equilibrium provides a game-theoretic model of strategic bidding in oligopolistic wholesale electricity auctions. This paper presents an intuitive account of current understanding and shows how welfare losses depend on the number of firms in the market and their asymmetry....

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,...

Wholesale electricity markets use different market designs to handle congestion in the transmission network. We compare nodal, zonal and discriminatory pricing in general networks with transmission constraints and loop flows. We conclude that in large games with many producers who are allowed to...

This paper considers the sealed bid and ascending auction, which both identifies the minimum Walrasian equilibrium prices and where truthful preference revelation constitutes an equilibrium. Even though these auction formats share many theoretical properties, there are behavioral aspects that...

This paper shows that in online car auctions, resellers are better at appraising the value of the cars they are bidding on than are consumers. Using a unique data set of online car auctions, I show that differences in bidding behavior between resellers and consumers can be explained by...

The afternoon effect, i.e., that prices in a sequence of auctions with identical items are decreasing with the order in which the auctions are terminated, is a frequently observed phenomenon in empirical auction studies. Using an unsurpassed amount of data from sequential online train ticket...

Capacity constraints on transmissions of electricity are raising an increasing policy concern as electricity markets are integrated around the world. But our understanding of the workings of such markets is still limited. The purpose of this paper is to highlight the impact of transmission...

We demonstrate how suppliers can take strategic speculative positions in derivatives markets to soften competition in the spot market. In our game, suppliers first choose a portfolio of call options and then compete with supply functions. In equilibrium firms sell forward contracts and buy call...