Revisiting minimum profit conditions in uniform price day-ahead electricity auctions

We examine the problem of clearing day-ahead electricity market auctions where each bidder, whether a producer or consumer, can specify a minimum profit or maximum payment condition constraining the acceptance of a set of bid curves spanning multiple time periods in locations connected through a transmission network with linear constraints. Such types of conditions are for example considered in the Spanish and Portuguese day-ahead markets. This helps describing the recovery of start-up costs of a power plant, or analogously for a large consumer, utility reduced by a constant term. A new market model is proposed with a corresponding MILP formulation for uniform locational price day-ahead auctions, handling bids with a minimum profit or maximum payment condition in a uniform and computationally-efficient way. An exact decomposition procedure with sparse strengthened Benders cuts derived from the MILP formulation is also proposed. The MILP formulation and the decomposition procedure are similar to computationally-efficient approaches previously proposed to handle so-called block bids according to European market rules, though the clearing conditions could appear different at first sight. Both solving approaches are also valid to deal with both kinds of bids simultaneously, as block bids with a minimum acceptance ratio, generalizing fully indivisible block bids, are but a special case of the MP bids introduced here. We argue in favour of the MP bids by comparing them to previous models for minimum profit conditions proposed in the academic literature, and to the model for minimum income conditions used by the Spanish power exchange OMIE

Investment incentives and auction design in electricity markets

Motivated by the regulatory debate in electricity markets, we seek to understand how market design affects market performance through its impact on investment incentives. For this purpose, we study a two-stage game in which firms choose their capacities under demand uncertainty prior to bidding into the spot market. We analyse a number of different market design elements, including (i) two commonly used auction formats, the uniform-price and discriminatory auctions, (ii) price-caps and (iii) bid duration. We find that, although the discriminatory auction tends to lower prices, this does not imply that investment incentives at the margin are poorer; indeed, under reasonable assumptions on the shape of the demand distribution, the discriminatory auction induces (weakly) stronger investment incentives than the uniform-price format

Demand Reduction and Inefficiency in Multi-Unit Auctions

Auctions typically involve the sale of many related goods. The FCC spectrum auctions and the Treasury debt auctions are examples. With conventional auction designs, large bidders have an incentive to reduce demand in order to pay less for their winnings. This incentive creates an inefficiency in multi-unit auctions. Large bidders reduce demand for additional units and so sometimes lose to smaller bidders with lower values. We demonstrate this inefficiency in several auction settings: flat demand and downward-sloping demand, independent private values and correlated values, and uniform pricing and pay-your-bid pricing. We also establish that the ranking of the uniform-price and pay-your-bid auctions is ambiguous. We show how a Vickrey auction avoids this inefficiency and how the Vickrey auction can be implemented with a simultaneous, ascending-bid design (Ausubel 1997). Bidding behavior in the FCC spectrum auctions illustrates the incentives for demand reduction and the associated inefficiency.Auctions; Multi-Unit Auctions; Spectrum Auctions; Treasury Auctions

Mixed Strategies in Discriminatory Divisible-good Auctions

Author: Edward J. Anderson, Pär Holmberg and Andrew B. Philpott Keywords: Pay-as-bid Auction; Divisible Good Auction; Mixed Strategy Equilibria; Wholesale Electricity Markets Pages: 71 Published: November 24, 2009 JEL-codes: D43; D44; C72 Download Wp814.pdf (756 kB) Abstract 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, and characterize mixed-strategy Nash equilibria for pay-as-bid auctions where demand is uncertain and costs are common knowledge; a setting for which pure-strategy supply function equilibria typically do not exist. We generalize previous results on mixtures over horizontal offers as in Bertrand-Edgeworth games, but more importantly we characterize novel mixtures over partly increasing supply functions.Pay-as-bid Auction; Divisible Good Auction; Mixed Strategy Equilibria; Wholesale Electricity Markets

Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords

We investigate the "generalized second price" auction (GSP), a new mechanism which is used by search engines to sell online advertising that most Internet users encounter daily. GSP is tailored to its unique environment, and neither the mechanism nor the environment have previously been studied in the mechanism design literature. Although GSP looks similar to the Vickrey-Clarke-Groves (VCG) mechanism, its properties are very different. In particular, unlike the VCG mechanism, GSP generally does not have an equilibrium in dominant strategies, and truth-telling is not an equilibrium of GSP. To analyze the properties of GSP in a dynamic environment, we describe the generalized English auction that corresponds to the GSP and show that it has a unique equilibrium. This is an ex post equilibrium that results in the same payoffs to all players as the dominant strategy equilibrium of VCG.

On-demand or Spot? Selling the cloud to risk-averse customers

In Amazon EC2, cloud resources are sold through a combination of an on-demand market, in which customers buy resources at a fixed price, and a spot market, in which customers bid for an uncertain supply of excess resources. Standard market environments suggest that an optimal design uses just one type of market. We show the prevalence of a dual market system can be explained by heterogeneous risk attitudes of customers. In our stylized model, we consider unit demand risk-averse bidders. We show the model admits a unique equilibrium, with higher revenue and higher welfare than using only spot markets. Furthermore, as risk aversion increases, the usage of the on-demand market increases. We conclude that risk attitudes are an important factor in cloud resource allocation and should be incorporated into models of cloud markets.Comment: Appeared at WINE 201

Political Cycles : The Opposition Advantage

We propose a two dimensional infinite horizon model of public consumption in which investments are decided by a winner-take-all election. Investments in the two public goods create a linkage across periods and parties have different specialities. We show that the incumbent party vote share decreases the longer it stays in power. Parties chances of winning do not converge and, when the median voter is moderate enough, no party can maintain itself in power for ever. Finally, the more parties are specialized and the more public policies have long-term effects, the more political cycles are likely to occur.Cycles, Alternation, Public goods, Advantage, Opposition

Liquidity risks on power exchanges

Financial derivatives are important hedging tool for asset’s manager. Electricity is by its very nature the most volatile commodity, which creates big incentive to share the risk among the market participants through financial contracts. But, even if volume of derivatives contracts traded on Power Exchanges has been growing since the beginning of the restructuring of the sector, electricity markets continue to be considerably less liquid than other commodities. This paper tries to quantify the effect of this insufficient liquidity on power exchange, by introducing a pricing equilibrium model for power derivatives where agents can not hedge up to their desired level. Mathematically, the problem is a two stage stochastic Generalized Nash Equilibrium and its solution is not unique. Computing a large panel of solutions, we show how the risk premium and player’s profit are affected by the illiquidity.illiquidity, electricity, power exchange, artitrage, generalized Nash Equilibrium, equilibrium based model, coherent risk valuation