This paper derives a Supply Function Equilibrium (SFE) of a pay-as-bid auction, also called discriminatory auction. Such an auction is used in the balancing market for electric power in Britain. For some probability distributions of demand a pure-strategy equilibrium does not exist. If demand...

Producers submit committed supply functions to a procurement auction, e.g. an electricity auction, before the uncertain demand has been realized. In the Supply Function Equilibrium(SFE), every firm chooses the bid maximizing his expected profit given the bids of the competitors. In case of...

In most electricity markets generators must submit step-function offers to a uniform price auction. These markets are often modelled as simpler pure-strategy Supply Function Equilibria (SFE) with continuous supply functions. Critics argue that the discreteness and discontinuity of the required...

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...

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...

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....

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...

Forward sales is a credible commitment to aggressive spot market bidding, and it mitigates producers' market power in electricity markets. Still it can be profitable for a producer to make such a commitment if it results in a soft response from competitors in the spot market (strategies are...

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 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....