Supply Function Auction for Linear Asymmetric Oligopoly: Equilibrium and Convergence

AbstractWe study the supply function auction for an asymmetric oligopoly with uncertain linear demand function and linear marginal cost functions of producers. We examine existence of a supply function equilibrium (SFE) in the model and convergence of the best response dynamics to this equilibrium. We show that the dynamics converges to the SFE for a duopoly, but in general the SFE and the strong best response do not exist in the model

Learning from past bids to participate strategically in day-ahead electricity markets

We consider the process of bidding by electricity suppliers in a day-ahead market context, where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other competing suppliers' bids. Based on the submitted bids, the market operator schedules suppliers to meet demand during each hour and determines hourly market clearing prices. Eventually, this game-theoretic process reaches a Nash equilibrium when no supplier is motivated to modify her bid. However, solving the individual profit maximization problem requires information of rivals' bids, which are typically not available. To address this issue, we develop an inverse optimization approach for estimating rivals' production cost functions given historical market clearing prices and production levels. We then use these functions to bid strategically and compute Nash equilibrium bids. We present numerical experiments illustrating our methodology, showing good agreement between bids based on the estimated production cost functions with the bids based on the true cost functions. We discuss an extension of our approach that takes into account network congestion resulting in location-dependent pricesFirst author draf

Learning from Past Bids to Participate Strategically in Day-Ahead Electricity Markets

We consider the process of bidding by electricity suppliers in a day-ahead market context where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other competing suppliers' bids. Based on the submitted bids, the market operator schedules suppliers to meet demand during each hour and determines hourly market clearing prices. Eventually, this game-theoretic process reaches a Nash equilibrium when no supplier is motivated to modify her bid. However, solving the individual profit maximization problem requires information of rivals' bids, which are typically not available. To address this issue, we develop an inverse optimization approach for estimating rivals' production cost functions given historical market clearing prices and production levels. We then use these functions to bid strategically and compute Nash equilibrium bids. We present numerical experiments illustrating our methodology, showing good agreement between bids based on the estimated production cost functions with the bids based on the true cost functions. We discuss an extension of our approach that takes into account network congestion resulting in location-dependent prices

Supply Function Equilibria Always Exist

Supply function equilibria are used in the analysis of divisible good auctions with a large number of identical objects to be sold or bought. An important example occurs in wholesale electricity markets. Despite the substantial literature on supply function equilibria the existence of a pure strategy Nash equilibria for a uniform price auction in asymmetric cases has not been established in a general setting. In this paper we prove the existence of a supply function equilibrium for a duopoly with asymmetric firms having convex costs, with decreasing concave demand subject to an additive demand shock, provided the second derivative of the demand function is small enough. The proof is constructive and also gives insight into the structure of the equilibrium solutions

Supply Function Equilibria Always Exist

Supply function equilibria are used in the analysis of divisible good auctions with a large number of identical objects to be sold or bought. An important example occurs in wholesale electricity markets. Despite the substantial literature on supply function equilibria the existence of a pure strategy Nash equilibria for a uniform price auction in asymmetric cases has not been established in a general setting. In this paper we prove the existence of a supply function equilibrium for a duopoly with asymmetric firms having convex costs, with decreasing concave demand subject to an additive demand shock, provided the second derivative of the demand function is small enough. The proof is constructive and also gives insight into the structure of the equilibrium solutions

混合寡占における価格数量の内生化に関する研究

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 松村 敏弘, 東京大学教授 小川 光, 東京大学教授 佐々木 弾, 東京大学教授 中林 真幸, 学習院大学教授 清水 大昌University of Tokyo(東京大学

CONTROL SYSTEM MODEL FOR ANALYSIS OF ELECTRICITY MARKET BIDDING PROCESS

This dissertation proposes a closed-loop control system model to facilitate mathematical analysis and promote operational efficiency of the dynamic bidding process. Electricity market deregulation has brought an innovation of the market structure and changed the electric power production from the old monopolistic way to a competitive market environment. Electricity is treated as a commodity and being traded among the market participants. The analysis of electricity market behavior becomes increasingly important and challenging. This dissertation develops a control-theoretic model to analyze and predict electricity market behavior. The model is based on the perspective of the power generation side (GENCOS) and ISO. The purpose is to achieve a rational profit maximizing behavior for GENCOS during the day-ahead bidding process and to improve the wholesale market efficiency. The control-theoretic model uses the game theory embedded with the learning ability as the major bidding strategy, which allows GENCOS to adjust their next-day bidding in the form of supply function equilibrium (SFE) through market observations. Recursive least square (RLS) method based on two ARMA models is introduced for demand and price forecasting in order to maximize the GENCO’s profit. This method is implemented into the bidding strategy of SFE with learning process. In order to better capture the demand and price dynamics beforehand, this dissertation also introduces an adaptive multiresolution prediction algorithm. This algorithm establishes a systematic structure to hierarchically decompose the original demand and price data into subtasks with different time frames, within which the data are able to be trained separately and efficiently. The real market data from New York Independent System Operator and PJM interconnection are used to demonstrate the effectiveness of the proposed model and training algorithm

Numerical Calculation Of An Asymmetric Supply Function Equilibrium With Capacity Constraints

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 asymmetric producers with general cost functions, previous work has shown that it is very difficult to find valid SFE. This paper presents a new numerical procedure that can solve the problem. It comprises numerical integration and an optimization algorithm that searches an end-condition. The procedure is illustrated by an example with three asymmetric firms