Two settlement stochastic auctions
1 Literature Review
1.1.1 Electricity markets
Scheweppe  for the first time introduced locational spot prices for a competitive electricity market. This paper showed that prices of a fully competitive electricity market is the same as prices coming out of an optimization problem that minimizes total cost of generation by taking into account generation cost of each of the firms in the electricity network. Equivalently, it means that in a competitive electricity market firms will o?er their real cost of generation and market will be cleared as this optimization problem suggests.
1.1.2 Forward contracts
 discussed how forward markets emerged in UK. This paper showed that Nuclear Energy Agreement (NEA), a long-term fixed contract between Scottish Nuclear and Scottish Power and Hydro-Electric, does not have anticompetitive e?ects despite what European Commission suggests. Several authors have investigated the aims of firms for participating in the forward markets. By taking part in the forward markets, generators and retailers can avoid risk of fluctuating spot market. Von der Fehr and Harbord (1992) used a multi-unit auction to show that generators desire to take part in a forward market to commit to produce more during peak demand periods. Green and Newbery (1992) examined a supply function model to account for formation of forward and spot markets. Using a Nash-Cournot spot market, one year later, Powell (1993) showed that risk neutral generators have incentive to participate in forward market if price is more in the forward market in comparison with the expected spot market price.
1.2 Two settlement deterministic auctions
1.2.1 Forward market as a Nash-Cournot game
Allaz and Vila (1993), Willems (2005) and Gans et al. (1998) [2, 24, 10] Showed that firms are desirous to take part in the forward market, while it increases demand and decreases prices.
Allaz and Vila  considered a two-settlement Cournot-Nash electricity market for the first time. They showed in their paper how a forward market could be formed based on an aggressive behaviour of firms to increase their market share. Their model illustrates how firms expose to Prisoner�s dilemma and finally loose profit. They show that existing of the forward market increases consumer welfare. Their analysis is based on the assumption that arbitrage is not possible in the market and this fact determines forward market price which is equal to expected value of the spot market price. Haskel and Powell (1994) extended Allaz and Vila�s analysis for a general conjectural variations. An important consideration which is not done here is considering repeated game and collusion as market repeats every period (e.g. 48 periods a day in New Zealand). In New Zealand generators is informed of o?er stack after ??? periods and as time interval is short, they discount factor is quite high and therefore collusive behaiviour is probable. a Gans et. al (98) also emphasised that existing a contract markert can increase competition in the spot market and so leads to highier prices. Willems (2005) replaced two-way contracts in Allaz and Vila�s model with call options ? and compared the consequences of these assumptions, such as market e?eciency. Later Bushnell (2007) extended Allaz and Vila�s model to an oligopoly and investigated the e?ects of forward contracting on the spot market. Su (2007) ?
1.2.2 Supply function equilibrium
One of the appropriate approaches to model electricity markets is using supply function equilibrium (SFE). Klemperer and Meyer (1989) applied SFE for the first time to model an oligopolistic market with firms o?ering supply functions where demand is un- certain. In 1992, Green and Newbery (92) exploited SFE to investigate the behaviour of firms in the England and Wales electricity market, after deregulation of England and Wales electricity market. They tried to use of a model of uncongested (one-node) two- settlement electricity market for predicting how much e?cient this deregulation was. In their model each generator o?ers a non-decreasing supply function indicating the price they are willing to be paid for each unit for di?erent amount of energy they produce.
They showed that a large amount of deadweight loss could be resulted from excess in investment and market power in short term until entrance of new generators to the com- petion. Newbery (1998) and Green (1999) consider a two-settlement electricity market by using SFE for the first time. They showed that contract market causes an increase in supply in the second stage of the market. Newbery (1998) uses this model to theorize the problem of entry to the English electricity market. He showed that when incumbants have enough capacity they can reduce price to the extent to prevent entrants from entry to the market. Having capacity constraints may prevent encombents from deterring entry. Green (1999) continued Newbery�s work by considering linear cost marginal cost function instead of constant marginal cost. Lien (2001) also worked on this issue and showed that forward contracting hardens new entry to the market and increases incumbent long time profit and e?ciency. Anderson and Philpott (2002) used a discontinious supply function with unknown demand and probabalistic firms be- haviour. They used this model to construct an optimal supply function curve for a firm in the presence of uncertainty and lack of full information. Anderson and Xu (2005) in addition to investigating necessary and su?cient conditions for optimality of the supply function equilibrium, focused on equilibrium of the two-settlement market and relation between these two stages. Anderson and Xu (2006) used a complicated SFE model for markets with option contracts ? and nonsmooth costs.
1.3 Two settlement stochastic auctions
Zhang et al. () proposed a two stage stochastic Nash-Cournot equilibrium prob- lem with equilibrium constraints. This means that their forward market equilibrium is constrained to the spot market equilibrium as a complementarity problem. Shanbhag (2005) investigates a two-settlement stochastic market for a two-node model. The model he considers in his investigation is a Nash-Cournot model. more? Von der Fehr and Harbord (92) used a two-settlement model with multiple demand scenarios and capacity constraints. They explained how spot prices could be reduced as an e?ect of contract forward market. They argued that willingness to increase contract quantity and to be dispatched in to their full capacity in most of the scenarios causes firms to take part in the contract market. In this settlement, Batstone (undated) also examined problem of uncertainty on cost of generation along with risk-neutral generators and risk-averse consumers and found that generators are willing to increase contract level and therfore selling more comodity by increasing risk of the spot market for consumers.
1.4 Optimisation and KKT conditions
For investigating network e?ects Yao et al. (2007) used a bilevel electricity market with KKT conditions along with network constraints as a maximization problem for firms. Hu and Ralph (2007) used equilibrium constraints to model a two-settlement electricity market. In their model both firms and consumers are players who bid cost and utility functions respectively and market clears by solving an optimization problem minimizing total cost. This is a network with several nodes. (? improtant, probably cournot ?)
Green and Newbery(92) : (used above) After deregulation of England and Wales elec- tricity market, Green and Newbery (92) tried to use of model of uncongested (one- node) two-settlement electricity market for predicting how much e?cient this deregula- the price they are willing to be paid for each unit for di?erent amount of energy they produce. They showed that a large amount of deadweight loss could be resulted from excess in investment and market power in short term until entrance of new generators to the competion.
Newbery (1995) discuss on problem of new entry to England and Wales electricity market. Green (1995) talk over the relation between competition and number of firms in the market.
Bolle (1992) looked into the di?erent ways of exposure of consumers to the market prices by using an SFE model. He concluded at the end that for increasing competition it is better that consumers be awared of the spot market prices.
Bolle (2001) added demand side bidding to his previous paper and worked on demand and supply functions in equilibrium.
Anderson and Bergman (1995) analysed Swedish electricity market when it was consisted of two main firms with Cournot-Nash and Bertrand models and concluded that it is not a good idea to privatize the market as equilibrium prices would be high and more firms are needed to have logical equilibrium prices.
Von der Fehr and Harbord (1993) debate on England and Wales electricity market with capacity constraints and step supply functions and find that mixed strategy equi- libria lead to higher prices in comparison with marginal prices. This results to ine?cient dispatch of the market. They have also used some empirical study based on at the time two major British generators to support waht they have theoretically shown.
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