Forward Contracts and Collusion in the Electricity Markets

Forward Contrats and Collusion in the Eletriity Markets Yanhua Zhang y University of Toulouse Otober 006 Abstrat European ompetition authorities intend to mitigate market power in eletriity markets by ompelling merging rms to sell virtual apaity to prospetive ompetitors. In the eonomi literature, Allaz and Vila (1993) argue that trading forward ontrats enhanes ompetition, whih is prevalently aepted by many artiles on eletriity market ompetition. However, this result does not hold with the framework of an in nitely repeated game. We nd that introduing forward trading allows rms to sustain ollusive pro ts forever. The obligation to sell more ontrats imposed by the regulator makes it more di ult for the inumbent rm to ollude taitly with its ompetitor. But this onlusion only holds when the ompetitor of the inumbent is a non-fringe rm and when the pro t sharing rule on the ollusive path is spei. Otherwise, trading forward ontrat either has no e et or possibly failitates tait ollusion if the ompetitor is a fringe rm. The analysis suggests that ompetition authorities should not only worry about the frequeny of trading forward ontrats, but also be areful with the regulation of ontrat quantity. Keywords: Contrat market, Eletriity, Spot Market, Forward, Tait ollusion. JEL Classi ation: C7 D3 G13 L13 L9 Support from the European Assoiation for Researh in Industrial Eonomis (E.A.R.I.E.), through the award of Paul Geroski Prize (Young Eonomists Essay Award) is gratefully aknowledged. I am grateful to Claude Crampes for many helpful omments and enouragement. I would also thank the setor ompetition and regulation at CPB (Netherlands Bureau for Eonomi Poliy Analysis) for its hospitality and, in partiular, Mahiel Mulder and Gijsbert Zwart for their help in the early stage of this researh. I thank all the seminar and onferene partiipants at the University of Paris IX-Dauphine, IAEE006 (Potsdam) and EARIE006 (Amsterdam) for their valuable omments. Any errors are of ourse my own. y Mailing address: Université de Toulouse, GREMAQ, MF01, 1 Allee de Brienne, 31000 Toulouse, Frane. Tel: +33 (0) 5615610. Fa: +33(0)56118637. Email: yanhua.zhang@univ-tlse1.fr 1

1 Introdution There is a widespread presumption among eonomists that forward trading is soially bene ial. Allaz and Vila (1993) argue that forward trading raises welfare even in the absene of any risk. They investigate the ase of Cournot duopolists and haraterize an equilibrium outome with larger outputs, hene a lower spot prie, ompared to the ase without forward trading. The point is that selling forward allows eah duopolist to ommit to a Stakelberg level of output in the spot market but, sine both do so in equilibrium, no one sueeds in aquiring a leader s advantage. As a result, ompetition is tougher in the spot market and welfare is improved, ompared to a situation without forward trading. Allaz and Vila also etend this result to the ase where there is more than one time period for forward trading. Without unertainty, they establish that as the number of periods of forward trading tends to in nity, produers lose their ability to raise market pries above marginal ost and the outome tends to the ompetitive solution. But it is still a hot topi to verify the robustness of Allaz and Villa s result. In the real world, there are roughly two kinds of forward ontrats: physial ontrat and nanial ontrat. In several merger ases in European eletriity markets, ompetition authorities have ordered dominant rms to sell speial forward ontrats, named virtual power plants (VPP), in order to redue the market power of large eletriity ompanies. The earliest VPP apaity autions were launhed by EDF in Frane in 001. As a national dominant power provider, EDF set out to aquire a substantial interest in the Germany-based vertial utility and eletriity trader EnBW in 000. Being judged to enjoy a dominant position by the European Commission, EDF had to ommit in an agreement with the European Commission to begin the virtual divestment of 6; 000 megawatts of generation apaity in 001, whih represented approimately 10% of Frane s eletriity supply. VPPs have also been used in Belgium for the aquisition by Eletrabel of the supply ativities of IVEKA in 003, one of the former assoiations of loal-governmentowned utilities ative in loal distribution grid operation and supply of both eletriity and gas. Now it is also disussed in the Netherlands, Denmark and Czeh Republi.

Those VPP ontrats are atually nanial ontrats, spei ally all options. In this paper, we will fous on physial forward ontrats instead of nanial ones. We would like to draw out the following pratial questions: does the introdution of the opportunity of forward trading failitate ollusion and to what etent an forward trading mitigate market power? One intuition is that ontrat length does in uene the e etiveness of the market power mitigation that results from the ontrat position. Clearly, an obligation to sell ten years ontrats seems to have a more robust e et on the ompany s inentives to raise pries than the obligation to sell daily ontrats eah day during ten years. Observe that the bene ts of eerising market power may be reaped both in the spot market, where the atual strategi behavior may take plae, and in the regulated ontrat market. In this ontrat market (whih would typially take the form of an aution market) potential buyers would base their willingness to pay on the epeted behavior of the inumbent, whih might be ooperation on the prie or quantity, or no ooperation at all along the ommerial trading periods. Allaz and Villa (1993) is the rst theoretial analysis of the ompetition enhaning e et of forward trading. Based on this idea, Green (1999) analyzes the ase of two dominant produers of eletriity who an raise spot pries well above marginal osts, whih is pro table for them in the absene of ontrats. If fully hedged, however, the generators lose their inentive to raise pries above marginal osts. In addition, ompetition in the ontrat market an lead the generators to sell ontrats for the greater part of their output. Empirially, Green nds that sine privatization British generators have indeed sold most of their energy in the ontrat market. Brandts, Pezanis-Christou and Shram (003) use eperiments to study the e ieny e ets of adding the possibility of forward ontrating to a pre-eisting spot market. They deal separately with the ases where spot market ompetition is in quantities and where it is in supply funtions. In both ases they ompare the e et of adding a ontrat market with the introdution of an additional ompetitor, hanging the market struture from a triopoly to a quadropoly. They nd that, as theory suggests, for both types of ompetition the introdution of a forward market signi antly lowers pries. The ombination of supply funtion ompetition with a forward market leads to high 3

e ieny levels. Meanwhile, Le Coq and Orzen (00) also eamine the A&V s predition in a ontrolled laboratory environment. They investigate how and to what etent the market institution and the number of rms a et ompetition, in theory and in their eperimental markets. Their ndings support the main omparative-stati preditions of the model but also suggest that the ompetition-enhaning e et of a forward market is weaker than predited. In ontrast, entry has a stronger ompetition-enhaning e et. Nevertheless, there is some ontroversy about A&V s result. Hughes and Kao (1997) nd that if the ontrat position is not perfetly observed by the other players, i.e., one s ontrat hoie has no in uene on the others strategy, then the rm has no more inentive to sell forward ontrats. Harvey and Hogan (000) and Kamat and Oren (00) doubt that the ompetition-enhaning e et holds if rms play the game repeatedly, as is undeniably the ase in most real markets. They argue that a dynami setting may enable rms to ommit to keeping their forward positions to a minimum. Moreover, Liski and Montero (005) onsider an in nitely-repeated oligopoly in whih at eah period rms not only serve the spot market by either ompeting in pries or quantities but also have the opportunity to trade forward ontrats. Contrary to the pro-ompetitive results of nitehorizon models, they nd that the possibility of forward trading allows rms to sustain ollusive pro ts that otherwise would not be possible. The result holds both for prie and quantity ompetition and follows beause (ollusive) ontrating of future sales is more e etive in deterring deviations from the ollusive plan than in induing the previously identi ed pro-ompetitive e ets. Ferreira (003) studies an oligopolisti industry where rms are able to sell in a futures market at in nitely many moments prior to the spot market. A kind of Folk theorem is established: any outome between perfet ompetition and Cournot an be sustained in equilibrium. However, the ompetitive outome is not renegotiation-proof and only the monopolisti outome is renegotiation-proof if rms an buy and sell in the futures market. These results suggest, ontrary to eisting literature, that the introdution of futures markets may have an anti-ompetitive e et. Mahen and Salanie (00) show that, buying forward (rather than selling) ommits a produer to set a higher spot prie in order to inrease the value of his position. Due to Bertrand ompetition in the spot market, the other produer reats by raising his prie, whih

inreases the pro t of the rst produer. In equilibrium, both produers buy forward and spot pries are raised above the levels reahed in the absene of forward trading. Therefore, duopolists soften ompetition through forward trading. Clearly, whether forward ontrats an enhane ompetition depends strongly on the setup of the game. Changing the assumptions of the game towards a slightly di erent diretion might dramatially hange the onlusion. As we have notied above, the Allaz and Villa s market power mitigating e et of forward ontrats is based on several ritial assumptions: perfet observation of forward ontrats, selling instead of buying ontrats, unrepeated game setting, rational epetation, Cournot ompetition and prisoner s dilemma. Atually Allaz even indiated in his dissertation that hanging the response assumption from ed quantity to ed market share would reverse the onlusion. This result ould also be found in Green (00) with supply funtion equilibrium. Meanwhile, it is well-known that the prisoner s dilemma may not hold if the game is played repeatedly. The repetition of interations will help, somehow, players to obtain ollusive outomes. Therefore, it is still ambiguous how forward ontrats in uene the players to eerise market power. The main result of the paper is the following: given that introduing forward trading allows rms to sustain ollusive pro ts for an in nite number of periods, we show that selling more ontrats, as imposed by the regulator, makes it more di ult for the inumbent rm to ollude taitly with its ompetitor. If we use the threshold of the disount fator in ollusion-sustainable onditions to measure the di ulty of ollusion, augmenting ontrat quantity will inrease this threshold, whih means, harming tait ollusion between rms. But this onlusion only holds when the ompetitor of the inumbent is a non-fringe rm and when the pro t sharing rule on the ollusive path is spei. Otherwise, trading forward ontrat either has no e et or possibly failitates tait ollusion if the ompetitor is a fringe rm. The analysis suggests that ompetition authorities should worry about the frequeny of trading forward ontrat and the regulation of ontrat quantity. Here we analyze two kinds of ompetition patterns: Cournot and Bertrand. There are two separating onditions in the model: whether the entrant rm is a fringe rm and 5

whether the entrant rm has its own prodution faility besides the forward ontrat it buys. On the one hand, forward trading makes it indeed more di ult for rms to sustain ollusion beause it redues the remaining non-ontrated sales along the ollusive plan. This is the pro-ompetitive e et of repeated forward trading like in the stati setting. On the other hand, it beomes less attrative for rms to deviate from the ollusive plan, sine forward ontrats redue the market share that a deviating rm an apture in the deviation period but the punishment is not milder than in the repeated single spot market. However, things are more ompliated when we onsider the ases where the entrant rm is a fringe rm and it has its own prodution faility. There are three papers whih are most related to our work. Liski and Montero (005) rst studied forward trading s e et on tait ollusion. In their model, duopolist rms are selling forward ontrat simultaneously on the market and there is no strategi and timing advantages for either rms. However, we let the inumbent rm sell forward ontrats to entrant rms and both ompete in the spot market afterwards. The strategies of sustaining tait ollusion are di erent from Liski and Montero (005). Shultz (005) and Zhang and Zwart (006) both study the reputation e et of virtual power plant ontrats and reommend shorter trading frequeny, i.e. longer ontrat durations, for European ompetition authorities. However, Shultz (005) analyzes virtual power plant ontrats based on the physial ontrat form. The reputation e et built through trading forward ontrats along in nite periods makes it easier for both rms to apture monopoly pro ts under ertain irumstanes. In our work, we fous on the physial forward ontrat, and nd that forward trading makes it more di ult for rms to sustain tait ollusion under both modes of market ompetition other than the reputation e et. But this result indeed depends not only on the sharing rule of monopoly pro t along the ollusive path, but also on whether the entrant owns its prodution failities and whether it is apaity onstrained. Under ertain onditions it might have no in uene on tait ollusion. Zhang and Zwart (006) use a signaling game approah to analyze the reputation e et. The inumbent rm s hoie on forward ontrat signals its private information on ost, whih might in uene the entrant rm s belief when it bids in the forward market. Their researh fouses on nite time periods and the strategy hoie is di erent from our results. 6

The remainder of this paper is organized as follows: In setion, we set up the model. Setion 3 and presents our results for repeated forward markets, in whih we separate the ases where the entrant is a fringe rm or a non-fringe rm, with or without a prodution faility, being apaity onstrained or without any prodution limit. We also distinguish the ases of Cournot ompetition and Bertrand ompetition. Setion 5 summarizes and onludes. The setup.1 The stati model We start with a stati model where the rms an only play the game one. Firm 1, the inumbent rm, is fored by the regulator to sell forward ontrat. In the rst stage of the game, rm bids the unit prie p f for the regulated quantity. We rst assume that the forward market is onduted through a ompetitive aution and there are su iently many potential bidders so that rm is only a fringe rm and a short term player. In the net setion, we will rela this assumption and analyze the situation where rm is no longer a fringe rm and beomes a long-term player. The timing is as follows: at stage 1 the ontrat quantity, whih is going to be traded in the forward market, is ed by the regulator. At stage 0 rm hooses to bid on prie. At stage 1 rm 1 and rm ompete in the spot market, either à la Cournot or à la Bertrand. In this stati model, we study the simplest ase where rm has no prodution faility so that it annot sell more than in the spot market. In addition, this forward quantity is relatively small ompared to the total demand and rm is onstrained by. By bakward indution we rst onsider the situation in stage 1. After the aution of forward ontrat, rm 1 and rm ompete in the spot market. The quantity sold by rm 1 in the spot market is denoted as q 1. The inverse demand funtion of the spot market is given by p(q) = a Q, where Q is the total prodution. Given that rm 7

has no prodution faility and sell all its apaity 1, the optimization problem of rm 1 in quantity ompetition is ma q 1 (a q 1 )q 1 q 1 + (p f ) (1) The prie of forward ontrats, p f, is determined through the aution in the forward market and has no in uene in the spot market. Firm 1 maimizes the pro t from the residual demand with respet to its own quantity q 1 in the spot market. The rst order ondition gives the best hoie of rm 1 onditional on : q mf 1 = a Here supersript mf stands for monopoly with a fringe rm. Therefore, the total prodution in the spot market is q mf 1 + = a + () The prie in the spot market is p mf = a + (3) Given the fat that rm has no own prodution faility and is onstrained by this small ontrat apaity, rm 1 ats as a monopolist. The result would be the same if rm 1 ould determine its optimal spot prie faing the residual demand. Indeed, ma p s (a p s )(p s ) + (p f ) () gives p s = a + = pmf Now we onsider the forward market. The prospetive bidders are rational and 1 We will hek that it is its best hoie This rational epetation is prevailing among the bidders. Suppose that we have at least two bidders 8

foreast the ompetitive equilibrium spot prie of the net period, onsequently, rm should get no pro t by buying and selling forward ontrats. Comparison of pro ts is shown in the following matri 3, where p M represents the monopoly prie p M = a+. At equilibrium, rm bids the forward prie p f equal to the epeted spot prie p mf. Firm 1 mf p M p Firm mf p M p 0 ( a ) ( a ) + 0 ( a ) ( a ) Diagram 3-1: Pro t Matri Lemma 1 When the fringe bidder ( rm ) has no prodution faility, there eists a unique regulated-monopoly perfet equilibrium, where rm bids p mf and the inumbent rm ( rm 1) plays the dominant strategy p mf : Proof. Suppose rm has hosen p mf. Then the best strategy for rm 1 is to hoose p mf beause it always earns more by hoosing p mf (in this ase rm 1 s pro t is than by hoosing p M (in this ase rm 1 s pro t is (a ) (a ) ) ). Then let us suppose rm has hoosen p M. Firm 1 s best strategy is to hoose p mf beause it always earns more by hoosing p mf (in this ase rm 1 s pro t is ase rm 1 s pro t is rm hooses, rm 1 prefers p mf. (a ) + ) than by hoosing pm (in this (a ) ). Therefore in this two-stage stati model, no matter what in the ontrat market and the one who wins the ontrat is rational. It will also epet the other one, or the rest of the ontrat bidders, is as rational as itself. None of them would like to bid a prie higher than the spot market prie and to lose money (get negative pro t) in order to favor the inumbent rm. 3 We leave the alulation to the readers for the other pro ts in the matri: rm s pro t an be obtained by the following formula = (p f p s ), where p f is the hoie of rm and p s is the hoie of rm 1. is presented in the south-western orner of eah ell. Firm 1 s pro t omes from () and is presented in the north-eastern orner of eah ell. 9

Now let us look at rm s hoie. Knowing that rm 1 always prefers p mf in the seond stage, rm will be happier if it hooses p mf, in whih ase rm earns zero, than hoosing p M, in whih ase rm gets negative pro ts : In summary, when the fringe bidder has no prodution faility, a unique regulatedmonopoly perfet equilibrium eists in this two-stage stati game, where both rms bid p mf. The total pro t that rm 1 an gain through selling its own quantity in the spot market and through selling ontrats in the forward market under the stati setting is = (a q mf 1 )q mf 1 + (p mf ) = (a ) It is obvious that selling forward ontrats redues the pro t of the monopoly inumbent and mitigates its market power. This ompetition enhaning e et in the stati model supports the regulator s poliy of ompulsory sale of forward ontrat by the inumbent monopoly generator. As we mentioned above, the ontrat quantity is relatively small and rm is onstrained by this apaity. We must hek whether rm is not better o when buying only a fration of. Bidding for the whole is pro table only if is less than the rm s best response to rm 1 s quantity in a Cournot game. In other words, must be less than the quantity a q 1 () = a a whih implies 0 < a + 3 Reall that the Cournot prie in this asymmetri duopoly ase, where one has marginal prodution ost but the other has no prodution ost, is p C = a+. From (3) we 3 see that the monopoly prie with a fringe rm p mf belongs to the interval (p C ; p M ]. 10

3 The repeated game with a fringe rm In this setion we have several bidding andidates in the forward market aution. We all them fringe rms beause they are all small and short-term players, and we study the ase where the inumbent autions o its forward ontrats repeatedly for an in nite number of periods t = 1; ; :::; 1. We adopt the timing pattern used in Liski and Montero (005): the spot market opens at odd periods (t = 1; 3; :::) and the aution market opens at even periods (t = 0; ; :::) and. This timing assumption implies that all spot markets are preeded by a forward market where the inumbent rm has the opportunity to sell forward ontrats. A fringe rm annot seure whether it will be the winner of the net period aution. Its objetive is to gain as muh as possible in eah individual period. It is not in its interest to withdraw apaity in order to sustain a higher prie in the spot market. Therefore, the fringe rm sells all the aquired apaity in the spot market and by our ompetitive aution assumption it always earns zero pro t (see Diagram 3-1: the pro t matri). However, the inumbent has the interest to raise the prie to a monopoly level sine it is a long-term player in this repeated game. Given that the aution is onduted in a ompetitive way, rm 1 would like to give the bidders an impression that it will arry out the monopoly result and it would like to sustain this reputation aross periods. We start with the ase where rm has no prodution faility and an sell at most. We will loose this assumption in the net setions. We rst look for the ondition under whih an equilibrium of the repeated game eists, where rm 1 earns monopoly pro ts in the market. On the ollusive path, rm 1 always sells (q M ) in the spot market and in the forward market at prie p M = a+. Therefore, it earns the monopoly pro ts through selling the ontrats along the in nite number of periods. We also assume that rm 1 ares about the sum of the disounted future pro ts. The per-period disount fator is denoted by p, where 0 < < 1, so the disount fator between two onseutive spot market openings is, whih failitates the omparison with pure-spot repeated games. 11

3.1 Firm has no prodution faility 3.1.1 Cournot ompetition When rm has no prodution faility and ompetes with rm 1 in quantity on the spot market, if rm 1 deviates from the ollusive path at period t, this deviation always happens in the spot market. The reasons are the following: rm 1 an deviate by either underutting its spot prie through inreasing its own spot prodution, or inreasing its forward sale. Here the forward sale is ed by the regulator and the inumbent rm annot hange it easily. Even if the inumbent rm ould deide the forward sale, it would never be pro table beause any deviation in the forward market would instantly be deteted by bidding rms who would pay no more than the net period spot market prie. If rm 1 deviates from the ollusive path and maimizes its pro t with respet to quantity, it is more pro table for rm to detet it on the forward market of period t + 1. Therefore, rm 1 will maimize the pro t from the residual demand ma q 1 (a q 1 )q 1 q 1 + (p f ) and we are bak to the stati equilibrium q mf 1 = a p mf = a + The deviation pro t earned by rm 1 is d 1 = (a q mf 1 )q mf 1 q mf 1 = (a ) In period t + 1, aution partiipants will only bid at prie p mf to hange their epetation that rm 1 always hooses the highest prie p M, after deteting rm 1 s deviation in the spot market of period t. This reation is equivalent to punishment. To summarize, the aution partiipants have the following epetations funtion (impliitly, they also 1

epet that the winner of the aution will sell units in the spot market) 8 < p M if p p e t 0 = p M 8 t 0 < t or t = 0 t = : p mf otherwise: On the punishment path, there are trigger strategy epetations, whih means, if rm 1 deviates from the monopoly path and oods the market with prie lower than p M, it will get punished as under the stati model given that the fringe rm has not its own prodution faility. We elude the ases where the partiipants in the aution ollude to bid pries varying from zero to (p mf "), where " is etremely small. Even though those punishments are muh harsher than in the former ase we talked above, we assume that the number of partiipants in the aution is su iently large for suh ollusion on bidding pries lower than p mf to be impossible. However, notie that if suh a ollusion among aution partiipants is possible, the inumbent will be punished muh harder than what we assume, and it will be even easier for rm 1 to sustain the monopoly outome. Therefore, the monopoly result is sustainable if and only if the following ondition is satis ed 1 (a ) 1 (a ) + (a ) + (a ) + 1 (a ) The left hand side of the inequality represents the monopoly ollusive pro t whih the inumbent rm aptures. The rst two terms on the right hand side of the inequality stand for the deviation pro t whih rm 1 an earn when it gets o the ollusive path, and the last term on the right hand side of the inequality is the disounted pro t of rm 1 when rm retaliates under trigger strategy. That inequality implies C = 1 (5) where C is de ned as the threshold of the disount fator above whih ollusion is sustainable in Cournot ompetition. In this linear demand model, the ompetition enhaning e et of forward trading 13

that eisted in the stati model vanishes sine it makes it easier to sustain ollusion than in the ase where there is no forward trading possibility. However, this results is speial beause it strongly depends on the linearity of the demand funtion. Results for a more general demand funtion are shown in Appendi A.1. 3.1. Bertrand ompetition Consider the ase where rms play prie ompetition in the spot market. Given that rm has no prodution faility, it an only ompete against rm 1 under its apaity onstraint, where < a+. Like in the former subsetion, if rm 1 deviates from the 3 ollusive path in the spot market of period t by harging p d 1 = arg ma f(p 1 )(a p 1 )g = a + = pmf in the following periods t + 1; :::; 1, aution partiipants pays p mf instead of p M. The deviation pro t earned by rm 1 in the spot market is d 1 = (a q mf 1 )q mf 1 q mf 1 = (a ) The monopoly result is sustainable if and only if the following ondition is satis ed 1 (a ) 1 (a ) + (a ) + (a ) + 1 (a ) whih implies B = 1 (6) where B is de ned as the threshold of the disount fator above whih ollusion is sustainable in prie ompetition with one agent apaity onstrained. We retrieve the same results as those of quantity ompetition. It is not surprising sine the fringe rm, i.e. rm, has no prodution faility and annot produe more than the ontrat quantity, whih onstrains prie ompetition. Therefore, on the The threshold of the disount fator in the standard Cournot ompetiton is 9 17, whih will be proved later in the proof of Proposition 1 1

punishment path, rm annot punish rm 1 for deviating as harshly as under Bertrand ompetition without apaity onstraint, where the prie is pushed down to the marginal prodution ost and none of the rms make pro ts along the post-deviation periods. In the meantime, the introdution of forward trading does not hange the di ulty of ollusion sine the threshold of the disount fator is idential to the one in standard Bertrand ompetition 5. Lemma When the fringe rm has no prodution faility and when it is a short run player, there eists a subgame perfet equilibrium, where the inumbent rm earns monopoly pro ts from both the ontrat and spot markets in eah period, if the disount fator eeeds the threshold C = 1 (resp. B = 1 ) whih is derived from (5) (resp. (6)). Proof. It is lear that when the fringe rm has no prodution faility and when it is a short run player, we retrieve the standard result that Cournot ompetition is equivalent to Bertrand ompetition sine rm has apaity onstraint and rm 1 maimizes its pro t from the residual demand. Proposition 1 In this spei repeated game, when the ontrat quantity is relatively small, introduing forward trading opportunity does not hange the level of di ulty to sustain ollusion if both rms ompete à la Bertrand in the spot market. However, introduing forward ontrat failitates ollusion if both rms ompete à la Cournot in the spot market. Proof. This threshold B oinides to the standard ollusion-sustainable threshold of Bertrand ompetition, whih is SB = 1 (Tirole (1988)). 1 (a ) 1 8 (a ) + 1 0 The left hand side of the inequality is the equally shared monopoly ollusive pro t whih one rm aptures. The rst term on the right hand side of the inequality stands for the deviation pro t whih one rm an earn when it gets o the ollusive path, and the 5 The threshold of the disount fator in the standard Bertrand ompetiton is 1, whih will be proved later in the proof of Proposition 1 15

seond term on the right hand side of the inequality represents the disounted pro t of one rm when its rival retaliates under trigger strategy. The inequality whih implies SB = 1 where SB is de ned as the threshold of the disount fator above whih ollusion is sustainable in the standard Bertrand ompetition without apaity onstraint. introdution of forward ontrat atually makes no di erene from the situation where there is no forward trading opportunity if both rms ompete à la Bertrand. The result for quantity ompetition an be easily veri ed by omparing C = 1 with the standard ollusion-sustainable threshold of Cournot ompetition SC = 9 : In fat, 17 1 (a ) 1 8 (a ) + 1 (a ) The equally shared monopoly ollusive pro t stays on the left hand side of the inequality. One rm s deviation pro t is presented through the rst term on the right hand side of the inequality and the disounted pro t under retalization is the seond term. inequality implies where SC SC = 9 17 9 The The is de ned as the threshold of the disount fator above whih ollusion is sustainable in the standard Cournot ompetition 3. Firm has prodution faility When rm has its own prodution faility, it will not be onstrained by the ontrat quantity. We assume that rm has the same marginal prodution ost as rm 1, i.e., and a large prodution apaity. If rm is a short run player and it annot seure that it will win the aution in the following suessive periods, rm has only the interest to maimize its short run pro t and will not oordinate with the inumbent rm to restrit its prodution in order to sustain the monopoly pro t. In other words, there is no monopoly subgame perfet equilibrium and the short run fringe rm will ompete 16

against the inumbent, in the same manner as in the stati model. Proposition When the fringe rm has its own prodution faility and behaves as a short run player, it is not possible to sustain ollusion in the forward market and in the spot market. Proof. In the spot market if both rms ompete in prie without any apaity onstraint, we will retrieve stati Bertrand results and the equilibrium spot prie is equal to the marginal prodution ost. Antiipating this equilibrium prie, none of the aution partiipants would like to bid more than in the forward market. On the other hand, if both rms ompete in quantity without any apaity onstraint in the spot market, we will retrieve stati Cournot results and the equilibrium prie is a+ 3, none of the aution partiipants would like to bid more than this Cournot prie in the forward market. The repeated game with a non-fringe rm In this setion, we suessively eamine the ase where rm has prodution faility and is not apaity onstrained, and the ase where rm has apaity onstraint. In eah ase, we will onsider di erent pro t sharing rules on the ollusive path beause of this hange of bargaining power for rm to get its share in this ollusion.1 Firm is not apaity onstrained.1.1 Cournot ompetition Suppose that rm is not a prie-taking fringe rm but an play strategially against rm 1. However, only rm 1 has the obligation to sell forward ontrats and rm only has the hoie to buy forward ontrats. In the seond stage, the two rms ompete against eah other in the spot market à la Cournot. When rm owns prodution faility and faes no apaity onstraint, the net proposition shows that forward trading opportunity may make ollusion di ult to sustain. 17

Lemma 3 The threshold of the disount fator that makes rm 1 inline to sustain ollusion is C 1 () = Proof. see Appendi A. 9(a ) 17(a )+96 : Lemma The threshold of the disount fator that makes rm inline to sustain ollusion is C () = Proof. see Appendi A. 9(a ) 17(a ) 96 : Proposition 3 When rms ompete in quantity in the spot market and rm has no prodution apaity onstraint, selling forward ontrat makes it more di ult for both rms to ollude than in the ase where there is no forward trading opportunity. Proof. The thresholds whih are determined in Lemma 3 and Lemma imply C > C 1. Therefore, the relevant threshold is C and ollusion only eists when C (), whih is regime C in gure 1. Reall from the proof of proposition (1) that, without ontrat market, the standard threshold to sustain ollusion in Cournot ompetition is 9 17 We an ompare it with the relevant threshold and get the result that C () > 9 17 when 0 < < a : Therefore, selling forward ontrat makes it more di ult for both rms 1 to ollude than in the ase where there is no forward trading opportunity. Remark 1 If the forward ontrat quantity is su iently small 0 < < a 1, introduing the forward trading opportunity inreases the di ulty for the rms to sustain tait ollusion and this argument an be utilized by regulatory authorities to mitigate market power. However, if the forward ontrat quantity is relatively large, i.e. a, the 1 ondition of sustaining tait ollusion does not hold any more and it is not possible for rm to ollude. In other words, when a has no e et on the di ulty of ollusion. 1, any inrease of the ontrat quantity The relationship between the volume of forward ontrat and the disount fator ; whih desribes the thresholds between ollusion inentive and ollusion deterrene, are presented in gure 1. Regime A stands for the regime where none of the rms would like 18

(a )/ δ 1 C B (a )/1 δ C A C 9/17 1 δ Figure 1: Collusion Regimes-Cournot Competition to partiipate into ollusion. Regime B stands for the regime where rm 1 is inlined to ollude but rm is not. Regime C stands for the regime where both rms would like to sustain ollusion..1. Bertrand ompetition We still stik to the ase where only rm 1 has the obligation to sell forward ontrats and rm only has the hoie to buy the forward ontrats and then ompete against rm 1 in the spot market. Now the seond stage ompetition is à la Bertrand. When rm has a prodution faility and faes no apaity onstraint, proposition shows that forward trading opportunity may make ollusion more di ult to sustain. Lemma 5 The threshold of the disount fator that makes rm 1 inlined to sustain ollusion is B 1 () = 1 Proof. see Appendi A.3 (a ) [(a ) + ] : Lemma 6 The threshold of the disount fator that makes rm inlined to sustain ollusion is B () = 1 + Proof. see Appendi A.3 : (a ) 19

Proposition When rms ompete in prie in the spot market and when rm faes no prodution apaity onstraint, selling forward ontrat makes it more di ult for both rms to ollude than in the ase where there is no forward trading opportunity. Proof. The thresholds whih are determined in Lemma 5 and Lemma 6 imply B > B 1. Therefore, the relevant threshold is B and ollusion only is feasible when B (), whih is regime C in gure. Reall that, without forward, the standard threshold to sustain ollusion in Bertrand ompetition is 1. Comparing it with the relevant threshold, we get the result that B () > 1 when 0 < < a. Therefore, selling forward ontrat makes it more di ult for both rms to ollude than in the ase where there is no forward trading opportunity. Remark If the forward ontrat quantity is su iently small 0 < < a, introduing the forward trading opportunity will inrease the di ulty for both rms to sustain tait ollusion and this argument an be utilized by regulatory authorities to mitigate market power. However, if the forward ontrat quantity is relatively large, i.e. a, for- ward trading opportunity has reahed its maimal e et on tait ollusion sine it is not possible to ollude for rm s interest and this oalition relationship annot be built up in any ase. Inreasing the quantity of forward ontrat has no e et on the di ulty to ollude and annot be utilized by regulatory authorities as the argument of market-power mitigation. The relationship between the forward ontrat quantity and the disount fator an be presented by gure. Regime A stands for the regime where none of the rms would like to partiipate into ollusion. Regime B stands for the regime where rm 1 is inlined to ollude but rm is not. Regime C stands for the regime where both rms would like to sustain ollusion.. Firm is apaity onstrained It is not di ult to predit that prie ompetition orresponds to quantity ompetition when rm faes prodution limitation. A short-run player whih has its own prodution 0

(a )/ 0.13(a ) δ 1 B B δ B A C 1/ 1 δ Figure : Collusion regimes -Bertrand Competition apaity will not partiipate into ollusion and will only maimize its short run pro t. Only the long-run player would like to partiipate into ollusion sine it ould get a share of monopoly pro t in future periods. Now it beomes ruial how to share the monopoly pro t between the rms on the ollusive path. If both rms are symmetri, a natural assumption is to share the monopoly pro t equally. Then rm who has no right to sell forward ontrat would like to buy zero forward ontrat. The reason is as follows: the only pro t earned by rm omes from (q )p M, where supersript M stands for monopoly on the ollusive path. Therefore, rm has an inentive to buy as few forward ontrats as possible in order to get most monopoly pro t on the ollusive path if rm buys forward ontrats at prie p M. If both rms are asymmetri and rm is smaller than rm 1, rm will be onstrained by its apaity q k o the ollusive phase. Another sharing rule is to split the monopoly pro t aording to the same ratio as on the punishment path. If rm is relatively smaller and is onstrained by its apaity on the punishment path, its best response to rm 1 s deviation is to produe at full apaity. Therefore, the market share on the punishment path depends on rm s apaity k, as well as the forward ontrat. We denote the market share of rm 1 (resp. rm ) by s 1 (resp. s ): s 1 (k ; ); s (k ; ) where s 1 (k ; ) + s (k ; ) = 1. On the ollusive path, both rm produe the ollusive monopoly quantities and ap- 1

ture the ollusive monopoly pro ts aording to their market shares q M 1 = s 1 Q M ; q M = s Q M (7) M 1 = s 1 M ; M = s M (8) where the monopoly quantity is Q M = a, and monopoly pro t is M = is (a ). On the punishment path, the best response of rm 1 after deteting rm s deviation q1 R (k ) = arg ma(a q 1 k )q 1 + (p f ) = a k q 1 where supersript R stands for the best response. From the rm 1 s objetive funtion we an nd that rm 1 produes (q 1 + ) but only sells q 1 in the spot market. However, rm 1 also aptures its pro t by selling ontrat in the forward market. Even though o ially rm sells quantity in the spot market, this ontrat quantity is atually sold by rm 1 through forward trading. Therefore, we should ount q R 1 (k ) + for rm 1 s quantity and k for rm s quantity in the alulation of their market shares (9) s 1 = s = q1 R (k ) + q1 R (k ) + k + k q1 R (k ) + k + : The market shares beome s 1 = a k + a + k + ; s = a k + k + and the punishment pro ts are P 1 = (a k ) ; P = (a k )k where supersript P stands for punishment.

The total pro t is P = P 1 + P = (a + k + )(a k ) and P 1 = s 1 P ; P = s P (10) On the ollusive path, aording to (8) rms prodution are q1 M = a k + a a + k + q M k a = a + k + (11) On the deviation path, the best response an be alulated in the same way as (9) if rm 1 deviates q1 D = q 1 (q M ) = a qm q = q M = (a ) (a + ) (a + k + ) The deviation pro t of rm 1 is D 1 = a q M 1 q 1 (q M ) q 1 (q M ) q 1 (q M ) p M (a ) a + D 1 = + a + k + (a ) (1) where supersript D stands for deviation. If the long-term player owns its prodution faility, the non-deviation ondition of rm 1 is whih an be simpli ed by using (10): 1 1 s 1 M D 1 + 1 P 1 ; 1 1 M D 1 s 1 + 1 P (13) 3

If rm deviates from the ollusion path, the best strategy it may apply is q = k + (1) At this time, rm 1 still produes q 1 = q M 1. Therefore, the prie on the deviation path is p D = a q M 1 q where q M 1 and q are given by (11) and (1). The orresponding deviation pro t for rm is D = a q M 1 k (k + ) k p M (a ) D = The non-deviation ondition of rm is whih an be simpli ed by using (10): s (k + ) (k + ) + 1 1 s M D + 1 (a ) k (15) 1 1 M D s + 1 P (16) All those results above an be summarized in the pro t matri of Diagram 3-6 6 In the pro t ell (q M 1 ; q D ), the southwestern part D is the deviation pro t that rm earns when it heats and it is shown by (15). The northeastern part 1 reprensents the pro t that rm 1 earns when rm deviates but rm 1 still produes ollusive quantity: a a 1 = (1 s 1 ) (k + ) s 1 a + s 1 Moreover, in the pro t ell (q1 D ; q M ), the northeastern part D 1 is the deviation pro t that rm 1 earns when it heats and it is shown by (1). The southwestern part reprensents the pro t that rm earns when rm 1 deviates but rm still produes ollusive quantity: a = s a 1 3 s s

Firm 1 P D M M q1 or q1 (if firm takes q ) q1 Firm q q or (if firm 1 takes ) P D M q1 M q P π π P π1 D π1 D π M π π 1 M π1 Diagram 3-: the pro t matri It is easy to verify that D 1 s1 > D s when < (a ) and k < 3(a ) 8. Therefore, the relevant inequality to determine the threshold of ollusion-sustainable disount fator is (13), whih we an rewrite as follows: (a ) a + + a + k + 1 1 (a ) + (a ) s 1 1 (a + k + )(a k ) s 1 From this inequality, we derive the threshold value of, denoted by K : Collusion is sustainable if and only if K = (a ) (a ) a + a +k + k a +k + + (a k ) + (a ) (17) As the formula beomes heavy-handed, we fous on the speial ase where a = 1 and = 0. (17) beomes K = 1+ 1+k + k 1+k + + (1 k ) + + Taking = 0:1 and plotting K on the vertial ais, we have the impat of k on the 5

y 1 0.75 0.5 0.5 0 0 0.05 0.05 0.075 0.1 k Figure 3: The role of k when = 0:1 (dot) and when = 0: (solid) disount fator K, whih is shown by the dot line in gure 3. The solid line in gure 3 shows the impat of k on the disount fator K when = 0:. Clearly it is muh easier to sustain tait ollusion between rm 1 and rm when rm s apaity onstraint k inreases. The intuition is the following: when rm s apaity onstraint k inreases, both rms beome more and more symmetri, sine it is easier to sustain tait ollusion when both rm s sizes are similar, we onverge to the standard tait ollusion results. Taking k = 0:1 and plotting K on the vertial ais (named ais y), we also get the impat of on the disount fator K, whih is shown by the dot line in gure. The solid line in gure shows the impat of on the disount fator K when k = 0:. Clearly it is more di ult to sustain tait ollusion between rm 1 and rm when forward ontrat quantity inreases. The intuition is the following: when rm s has apaity onstraint k in the spot market, selling more forward ontrat will make the inumbent rm oupy more market share, whih inreases asymmetry between the inumbent and the entrant. Therefore it is more di ult to sustain tait ollusion when we have more asymmetri rms, as established by standard tait ollusion results. Conjeture 1 When rms have opportunity to trade forward ontrats, i.e. when is di erent from 0, it is easier to sustain tait ollusion when rm s apaity inreases. Moreover, when rm has a limited prodution apaity, it is more di ult to sustain 6

y 1 0.75 0.5 0.5 0 0 0.05 0.05 0.075 0.1 Figure : The role of when k = 0:1 (dot) and when k = 0: (solid) tait ollusion when forward ontrat quantity is larger. Remark 3 More eamples an be analyzed by denoting = k. Figure 5 shows the impat of on the disount fator K when rm s apaity is either k = 0:03 or k = 0:1. Those numerial results show that, when rm faes apaity onstraints, regulatory authorities may prefer selling more forward ontrats in order to inrease the di ulty for the two rms to sustain tait ollusion..3 Two entrant rms bid forward ontrats Let us etend the model to two entrant rms, denoted as rm i and rm j, ompeting to obtain the forward ontrat o ered by the inumbent rm. We assume that ommuniation is forbidden between rm i and rm j, and they annot ollude either taitly or publily. In the forward market, eah bidding rm would like to submit the highest bid that it believes will seure the ontrat, taking into aount the likely bid of the rival. Any bid lower than the rival s bid will make the bidding rm lose the aution. Therefore, ompetition for forward ontrats does not neessarily inrease as the number of entrant rms inreases. As long as there are at least two rms apable of making redible bids, ompetition an be as vigorous with two rms as with three or more. This is the 7

delta 1 0.75 0.5 0.5 0 0 0.5 1 1.5 alpha Figure 5: The impat of on the disount fator 3 when k = 0:03 (solid); k = 0:1 (dot) famous argument "Two Is Enough" onerning ompetition in bidding markets. Then we are bak to the ompetitive aution ase and will retrieve the same results whih are analyzed in setion 3 the repeated game with a fringe rm. 5 Conlusion We have studied the e et of trading forward ontrats on tait ollusion. Speially we have analyzed forward ontrat as a novel and uninvestigated feature in major merger ases. European ompetition authorities intend to mitigate market power by ompelling the merging rm to sell forward ontrats to prospetive ompetitors in the spot market. We have shown that under ertain onditions selling more ontrats, whih are imposed by the regulator, makes it more di ult for the inumbent rm to ollude taitly with its ompetitor. But this onlusion only holds when the ompetitor of the inumbent is a non-fringe rm and when the pro t sharing rule on the ollusive path is spei. Otherwise, trading forward ontrat either has no e et or possibly failitates tait ollusion if the ompetitor is a fringe rm. The analysis suggests that ompetition authorities should worry about both the frequeny of ontrat trading and the regulation of ontrat quantity. 8

A Appendi A.1 Solutions of the general reverse demand funtion We still keep the same timing pattern for the repeated game as what is disussed in setion 3.1. Assume the inverse demand funtion is p = D(q) and the ost funtion is C(q), where C 0 (q) > 0 and C"(q) > 0. The simplest ase will start with the one where rm has not its own prodution faility and an only sell up to the ontrat quantity. On the ollusive path, rm 1 will apture all the monopoly pro t not only by selling monopoly prie p M in the spot market, but also by selling monopoly prie p M in the forward market. Firm 1 maimizes the pro t faing the total demand ma q 1 D(q 1 )q 1 C(q 1 ) (18) The rst order ondition gives D 0 (q 1 )q 1 + D(q 1 ) = C 0 (q 1 ) (19) q M 1 an be driven out from (19) and the monopoly prie p M is solved by the the inverse demand funtion D(q M 1 ). Firm 1 obtains the pro t M = D(q M 1 )q M 1 C(q M 1 ) As the same reason as before, if rm 1 deviates from the ollusive path at period t, it always happens in the spot market, denoted t spot. Therefore, rm 1 will maimize the pro t faing the residual demand ma q 1 D(q 1 + )q 1 C(q 1 + ) + p f (0) The rst order ondition gives D 0 (q d 1 + )q 1 + D(q d 1 + ) = C 0 (q d 1 + ) (1) 9

The deviation pro t earned by rm 1 is d 1 = D(q d 1 + )q d 1 + D(q M 1 ) C(q d 1 + ) In period t + 1, aution partiipants will only bid at prie p S to punish rm 1, where p S is solved by using (1), after deteting rm 1 s deviation in period t spot. Firm 1 only gets P 1 on the suessive punishment path P 1 = D(q d 1 + )(q d 1 + ) C(q d 1 + ) To summarize, the aution partiipants have the following epetations funtion (impliitly, they also epet that the winner of the aution will sell units in the spot market) 8 < p M if p p e t 0 = p M 8 t 0 < t or t = 0 t = : p mf otherwise: On the punishment path, there are trigger strategy epetations, whih means, if rm 1 deviates from the monopoly path and oods the market with prie lower than p M, it will get punished as under the stati model given the fringe rm has not its own prodution apaity. We also elude the ases that the partiipants in the aution ollude to bid the pries varying from zero to (p S "), where " is etremely small. Even though those punishments are muh more harsh than the ase we talked above, we assume that the number of partiipants in the aution is su iently large that suh ollusion on bidding lower pries than p S is not possible. Notie that, however, if suh kind of ollusion among aution partiipants is possible and the inumbent rm, i.e. rm 1, thus will be punished muh harder than what we assume, it will be even easier for rm 1 to sustain the monopoly result. Therefore, the monopoly result is sustainable if and only if the following ondition is satis ed 1 1 M d 1 + 1 P 1 30

whih implies M 1 = d 1 d 1 P 1 () () an be further simpli ed as the following inequality 1 = D(qM 1 ) q d 1 + q M 1 C(q d 1 + ) C(q1 M ) D(q1 M ) D(q1 d + ) q1 d D(q1 M ) D(q1 d + ) A. Proof of Lemma 3 and Lemma Proof. As we have analyzed above, a short-run player whih has its own prodution apaity will not partiipate into ollusion and will only maimize its short run pro t. Only the long-run player would like to partiipate into ollusion sine it an get the monopoly pro t along the following suessive periods. Now it beomes ruial how to share the monopoly pro t between the rms on the ollusive path. If both rms are symmetri, a natural assumption is to share the monopoly pro t equally. But here rm 1 is the inumbent and is fored to sell quantity. Even though rm is big enough to ompete against rm 1 in the spot market without any apaity onstraint, it is always an entrant in the market and has less bargaining power in the arve-up of monopoly pro ts. First, we disuss the ase where rm has no apaity limit and it an produe whatever it wants. When is small enough, i.e. < (a ), rm 1 and rm will sell a total of monopoly quantity Q M = q C 1 + q C = a in the spot market on the ollusive path. Firm 1 has to sell quantity to rm in the forward market and realizes part of its monopoly pro t through forward ontrating. Therefore, in the arve-up of the whole monopoly pro t, rm 1 produes q C 1 = (Q M =+) and rm produes q C = (Q M = ). In eah period, rm 1 s pro t on the ollusive path is (p M )(Q M = + ) = ( a a ) + When rm 1 deviates in the spot market t, rm still produes q C and sells (q C +). 31