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    Holmberg, Pär. “Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints.” In, 2009. Publisher's VersionAbstract
    Producers submit offer curves to a procurement auction, e.g. an electricity auction, before uncertain demand has been realised. In the supply function equilibrium (SFE), every firm commits to the offer curve that maximises its expected profit, given the offer curves of competitors. The equilibrium is given by a system of differential equations. In practice, it has been very difficult to find valid SFE, i.e. non-decreasing solutions, from this system, especially for asymmetric producers. This paper shows that valid SFE can be calculated by means of a shooting algorithm that combines numerical integration with an optimisation procedure that searches for an end-condition. Multiple/parallel shooting is used for ill-conditioned cases.
    Holmberg, Pär. “Unique Supply Function Equilibrium with Capacity Constraints.” Energy Economics 30, no. 1 (2008): 147-172. Publisher's VersionAbstract
    Consider a market where producers submit supply functions to a procurement auction with uncertain demand, e.g. an electricity auction. In the Supply Function Equilibrium (SFE), every firm commits to the supply function that maximises expected profit in the one-shot game given the supply functions of competitors. A basic weakness of the SFE is the presence of multiple equilibria. This paper shows that with (i) symmetric producers, (ii) perfectly inelastic demand, (iii) a price cap, and (iv) capacity constraints that bind with a positive probability, there exists a unique, symmetric SFE.
    Genc, Talat, Suvrajeet Sen, and Stanley Reynolds. “Dynamic Oligopolistic Games Under Uncertainty: A Stochastic Programming Approach.” Journal of Economic Dynamics and Control 31, no. 1 (2007): 55-80. Publisher's VersionAbstract
    This paper studies several stochastic programming formulations of dynamic oligopolistic games under uncertainty. We argue that one of the models, namely games with probabilistic scenarios (GPS), provides an appropriate formulation. For such games, we show that symmetric players earn greater expected profits as demand volatility increases. This result suggests that even in an increasingly volatile market, players may have an incentive to participate in the market. The key to our approach is the so-called scenario formulation of stochastic programming. In addition to several modeling insights, we also discuss the application of GPS to the electricity market in Ontario, Canada. The examples presented in this paper illustrate that this approach can address dynamic games that are clearly out of reach for dynamic programming, a common approach in the literature on dynamic games.
    Murphy, Frederic, and Yves Smeers. “On the Impact of Forward Markets on Investment in Oligopolistic Markets with Reference to Electricity. Part I: Deterministic Demand.” In, 2007.Abstract
    murphy_and_smeers_paper_june_15_07.pdf

    Murphy, Frederic and Yves Smeers. On the Impact of Forward Markets on Investment in Oligopolistic Markets with Reference to Electricity. Part I: Deterministic Demand. 15 June 2007, 38 pages.

     

     

    This paper analyzes the properties of three capacity games in an oligopolistic market with Cournot players and deterministic demand. In the first game, capacity and the operation of that capacity is determined simultaneously. This is the classic open-loop Cournot game. In the second game, capacity is decided in the first stage and the operation of that capacity is determined in the second stage. The first-stage decision of each player is contingent on the solution of the second-stage game. This is a two-stage, closed-loop game. We show that when the solution exists, it is the same as the solution in the first game. However, it does not always exist. The third game has three stages with a futures position taken between the capacity stage and the operations stage and is also a closed-loop game. As with the second game, the equilibrium is the same as the open-loop game when it exists. However, the conditions for existence are more restrictive with forward markets added. When both games have an equilibrium, the solution values are identical. The results are very different from games with no capacity stage as studied by Allaz and Vila (1993), where they concluded that forward markets can ameliorate market power.

     

    Murphy, Frederic, and Yves Smeers. “On the Impact of Forward Markets on Investments in Oligopolistic Markets with Reference to Electricity. Part II: Uncertain Demand.” In, 2007. Publisher's VersionAbstract
    murphy_and_smeers_june_18_07.pdf

    Murphy, Frederic and Yves Smeers. On the Impact of Forward Markets on Investments in Oligopolistic Markets with Reference to Electricity. Part II: Uncertain Demand. 18 June 2007, 39 pages.

     

     

    There is a general agreement since Allaz-Vila’s seminal contribution that forward contracts mitigate market power on the spot market. This result is widely quoted and elaborated in studies of restructured power markets where it is generally believed that generators tend to exploit the special characteristics of this industry in order to extract higher prices. Allaz-Vila established their result under the assumption that the production capacities of the players are infinite. This assumption might have applied to the power industry in the early days of restructuring but it no longer holds in today environment of tightening capacity. We show that the Allaz-Vila result no longer holds when capacities are endogenous and constraining generation. Specifically the future market can enhance or mitigate market power when capacities are endogenous and demand is unknown at the time of investment. This result complements Part 1 where the authors show that forward markets do not mitigate market power when capacities are endogenous and demand is known at the time of investment. It also complements other work by Grimm and Zoettl who show that forward markets systematically enhance market power in some symmetric capacity-constrained markets.

     

    Hogan, William W., and Susan Pope. “United States of America Before the Federal Regulatory Commission: Comments on Wholesale Competition in Regions with Organized Electric Markets.” In, 2007.Abstract
    wwh_slp_ferc_091707.pdf

    Excerpt from the Introduction: 

    The Federal Energy Regulatory Commission is considering potential reforms to improve the operation of organized wholesale electric markets. The purpose of this paper is to discuss a larger framework for evaluating issues of regulation and market design in electricity markets. Regulation and competition are essential elements of electricity policy. The special requirements of electricity systems create a dual challenge: First, regulation must address issues of market design; markets cannot solve the problem of market design. Second, regulation must complement competition; inconsistent choices in either can undermine the foundations of reliable electricity supply at market prices and subvert the goals of organized electricity markets.

    Organized electricity markets are developing with many advanced features that address the technical requirements of electricity systems. Initial defects in market design are being addressed in a continuous process of learning and improvement. As experience accumulates, inevitably problems arise that present challenges for regulators. In some cases, the problems can be addressed through the use of markets and incentives. In other cases, the problems require regulation and mandates. A critical task for the regulator is to provide a proper balance of regulation and markets. This challenge is complicated through the unintended consequences of decisions in each realm. Market design can have significant effects on the outcome of regulation. In turn, regulation can have significant effects on the operation of markets. Whenever regulators must act, there is a choice in the type of action. Big “R” regulatory solutions often call for mandates and subsidies for favored programs. Little “r” regulatory solution would emphasize reforms of market design to improve incentives or limits on regulatory mandates to support rather than replace market choices. Regulation may be unavoidable, but there is flexibility in the type of regulation.

    A framework for evaluating issues of regulation and market design in electricity markets helps regulators identify regulatory choices that minimize the unintended consequences in markets, and identify market design features that can support the goals of regulation. A concern is that major regulatory decisions are being made without consideration of the interaction with markets and market design. The result is both a failure to resolve the immediate problems and collateral damage to operation of the market. The cycle precipitates more problems and more need for regulatory mandates to counter the effects of poor incentives in market design.

    This is an avoidable problem. The discussion here illustrates the type of problems that arise in organized markets and provides examples of innovative approaches addressing the problems that balance regulation and market design.

    Hochstetter, Sandra. “The Changing Landscape for Retail Procurement: from Restructured to Re-Regulated, and from Regulated to Government-Controlled.” In, 2007.Abstract
    sandy_hochstetter_remarks.pdf

    The Year 2007 has brought new legislative and regulatory challenges for all states --- both regulated and restructured --- and some of these challenges are affecting resource evaluation processes, and corresponding resource decisions, for the ultimate load-serving entities. The 2 most challenging legislative and business issues today ---- layered on top of continuing discontent with competitive market design and competitive procurement --- are the looming debates over mandated Renewable Portfolio Standards and mandated CO2 emission reductions. These frenzied discussions have led some policymakers and activists to call for a moratorium on new coal plants and the retirement of existing ones, along with a dogmatic focus on renewables and energy efficiency as the primary sources for new power supply. So --- it’s not just the restructured states that are undergoing political upheaval and second-guessing with respect to how electricity is provided to customers.

     Whether you reside in a vertically integrated, rate-regulated, and cost-of-service ratemaking jurisdiction, OR a "retail competition" state that is undergoing some type of transformation back to a more regulated service obligation and pricing regime, you are facing changes in the way that federal and state legislators, and various activist groups, expect you to manage your electric generation portfolio.

    The premise of my remarks today, which is a conclusion that I have reached during the past several months, is that I'm not sure how much of a "competitive market" or even a self-directed future I see for any retail service provider ---- no matter what state you're in or what type of regulatory framework you have.

    This new, unilateral focus on environmental issues is obscuring the laws of physics --- with respect to how the electricity grid works and what it takes to keep the lights on --- and the laws of economics --- with respect to what electricity costs, based on the fuel source used. My overall prediction is, if our hands are tied by the passage of very specific government-mandated generation portfolio standards, and laws that impose penalties on the consumption of specific fuels, we will be dealing with reliability problems in all states, a deviation from “least cost purchasing” standards in traditional states, and a significant reduction in market-driven resource decisions in restructured states.

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