Financial contracts as coordination device

Le Coq, Chloé; Schwenen, Sebastian Article — Published Version Financial contracts as coordination device Journal of Economics & Management Strategy Provided in Cooperation with: John Wiley & Sons Suggested Citation: Le Coq, Chloé; Schwenen, Sebastian (2020) : Financial contracts as coordination device, Journal of Economics & Management Strategy, ISSN 1530-9134, Wiley, Hoboken, NJ, Vol. 29, Iss. 2, pp. 241-259, https://doi.org/10.1111/jems.12340 This Version is available at: https://hdl.handle.net/10419/230025 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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J Econ Manage Strat. 2020;29:241–259. wileyonlinelibrary.com/journal/jems | 241 Received: 11 February 2019 | Revised: 11 October 2019 | Accepted: 23 December 2019 DOI: 10.1111/jems.12340 ORIGINAL ARTICLE Financial contracts as coordination device Chloé Le Coq 1,2 | Sebastian Schwenen 3,4,5 1 University of Paris II Panthéon‐Assas (CRED), Paris, France 2 Stockholm School of Economics (SITE), Stockholm, Sweden 3 School of Management, Technical University of Munich, Munich, Germany 4 German Institute for Economic Research DIW Berlin, Berlin, Germany 5 Mannheim Institute for Sustainable Energy Studies (MISES), Mannheim, Germany Correspondence Sebastian Schwenen, School of Management, Technical University of Munich, Munich, Germany. Email: [email protected] Funding information Energiforsk research program EFORIS; Marianne and Marcus Wallenberg foundation Abstract We study the use of financial contracts as bid‐coordinating device in multi‐unit uniform price auctions. Coordination is required whenever firms face a volunteer's dilemma in pricing strategies: one firm (the “volunteer") is needed to increase the market clearing price. Volunteering, however, is costly, as inframarginal suppliers sell their entire capacity whereas the volunteer only sells residual demand. We identify conditions under which signing financial contracts solves this dilemma. We test our framework exploiting data on contract positions by large producers in the New York power market. Using a Monte Carlo simulation, we show that the contracting strategy is payoff dominant and provide estimates of the benefits of such strategy. KEYWORDS auctions, coordination, electricity, forward markets, volunteer's dilemma JEL CLASSIFICATION D21; D44; L41; L94 1 | INTRODUCTION A variety of goods and services are traded in multi‐unit auctions. Classic examples include auctions for government bonds (Hortaçsu, Kastl, & Zhang, 2018), spectrum rights (Cramton & Ockenfels, 2017), electricity (Fabra, von der Fehr, & Harbord, 2006), emission allowances (Lopomo, Marx, McAdams, & Murray, 2011), or gas pipeline capacity (Newbery, 2002). The majority of multi‐unit auctions clear at a uniform price, which facilitates market entry (Ausubel, Cramton, Pycia, Rostek, & Weretka, 2014). Depending on the market architecture, bidders may also take financial positions on forward markets before participating in the auction. The theoretical literature on strategic forward trading shows that forward contracts affect spot market prices, either by enhancing or softening spot market competition (e.g., Allaz & Vila, 1993; Mahenc & Salanié, 2004). An example that seems to contradict the extant findings, however, was observed in the New York power market, which operates as a multi‐unit uniform price auction. Whereas two major producers signed forward contracts in 2006, the market price stayed equal to the regulatory price cap before and after the contract start date. Both the U.S. Federal Energy Regulatory Commission (FERC) and the Department of Justice (DOJ) investigated whether the contractual agreements constituted market manipulation. Their findings differed significantly. FERC (2008) argued against market manipulation and concluded that the contracts were instruments to hedge price risk. DOJ (2010), following Cramton (2007), found that the contracts helped firms to avoid competitive bidding strategies. ----------------------------------------------------------------------------------------------- This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Drawing from this case, we present a new theoretical framework to examine how forward contracts allow firms to coordinate on one of multiple equilibria in the spot market. Previous findings on the strategic use of forward contracts illustrate how firms use contracts to gain additional market share, leading to lower spot prices (Allaz & Vila, 1993) or how firms use contracts to increase spot prices (Mahenc & Salanié, 2004). We thus offer a new rationale for signing forward contracts, which is to avoid miscoordination in pricing strategies. We also contribute with an empirical investigation of this rationale. So far, the extent empirical literature on strategic forward contracts has shown price‐ reducing effects of forward contracts (e.g., Wolak, 2003) and strategic price premia on forward markets (Ito & Reguant, 2016). To our knowledge, empirical findings on price coordination through forward contracts have not been documented so far. We apply and test our model using rarely observed data on firms' financial positions from the case investigated by FERC and DOJ. Simulating market outcomes with and without contracts, we show that forward positions rule out competing (off‐)equilibrium outcomes and allow firms to coordinate on their pricing strategies. For our theoretical analysis, we model a standard multi‐unit uniform price auction. The literature on multi‐unit auctions considers continuous bid functions (e.g., Hortacsu & Puller, 2008; Klemperer & Meyer, 1989; Wilson, 1979) and discrete bids (e.g., Fabra et al., 2006; Kastl, 2006, 2012). Moreover, Kastl (2012) finds that as the number of steps increases, equilibrium conditions for discrete and continuous supply functions converge. In line with previous auction literature applied to electricity markets (e.g., Fabra et al., 2006; Reguant, 2014; Schwenen, 2015), we however focus on discrete bids as they well resemble the market environment that we study. Specifically, we model two large firms and a competitive fringe. Before auction clearing, the two large firms can sign forward contracts with a financial intermediary. If neither firm's capacity is sufficient to satisfy full demand, all pricing equilibria are characterized by one pivotal firm that clears the auction. This price‐setting firm can charge a supra‐competitive price due to its market power vis‐á‐vis residual demand. Yet, the firm compromises on selling parts of its capacity, similarly to how a standard monopoly firm would. Due to the institutional setup in the New York power market, we model a game of complete information. 1 As Le Coq, Orzen, and Schwenen (2017) point out, firms in such a game face a coordination problem akin to the volunteer's dilemma (Diekmann, 1985; Goeree, Holt, & Smith, 2017): one firm (the “volunteer”)isneededtoincrease the market clearing price. 2 Volunteering, however, is costly, as inframarginal suppliers sell their entire capacity whereas the volunteer only supplies residual demand. Our model illustrates conditions under which signing financial contracts solves this dilemma. More precisely, we show that signing opposite forward contracts increases both firms' profits when firms face the volunteer's dilemma. The contracts work as follows. The volunteering firm holds a long position, while the nonvolunteering firm holds a corresponding short position. By holding a long position, the volunteer obtains the high clearing price not only for its spot sales, but also for its financially contracted quantity. The other (“free‐riding”)firm,while losing money via the contract, benefits as it sells full capacity with certainty, knowing that its rival volunteers. We test our theoretical predictions by analyzing pricing strategies and contract choices in the New York power market. Focusing on this market offers several advantages. First, the fundamentals of this market, for example, on marginal costs, are in line with the characteristics of our model. Furthermore, the market was highly concentrated during our period of observation, which corresponds to our model with dominant and fringe firms. Moreover, our setting allows for exploiting detailed data on demand curves and firm capacities. Finally, given that the contracts at stake were publicly investigated, we can make use of detailed information on underlying contract positions. For our empirical analysis, we conduct a Monte Carlo simulation of market outcomes with and without observed contracts. We first show that, without contracts, the two largest firms would face a volunteer's dilemma: There exist two types of equilibria, in each of which one firm volunteers. Second, in line with our predictions, we find that the contract positions ruled out one of the two types of competing equilibria of the volunteering game. Third, we show that firms' contracting strategies were weakly payoff dominant, even at constant clearing prices before and after the contract start date. Our empirical investigation further illustrates that profits obtained via the forward market were just sufficient to achieve commitment and to reward the price‐setting firm for its volunteering role. Our paper is closely related to the literature on strategic interaction in forward and spot markets as pioneered by Allaz and Vila (1993). Starting from an oligopoly equilibrium on the spot market, they prove a competition‐enhancing effect of forward markets. However, whether contracting triggers aggressive pricing behavior depends crucially on the institutional and structural market features, for example, on whether market participants interact repeatedly 1 Demand, firm capacities, and also bids submitted to the auction are published ex‐post and hence firms can infer and learn about their competitors' forward and spot sales. We also assume that contract positions of the dominant firms are common knowledge. This is in line with our empirical case, where the financial intermediary publicly searched for counterparties for the contract and later was accused of coordinating financial flows, having to pay 4.8 USD million in disgorgement (DOJ, 2012). 2 Alternatively, the volunteer's dilemma can be interpreted as an N‐person battle of the sexes. 242 | LE COQ AND SCHWENEN (Liski & Montero, 2006), on the distribution of contracts among firms (de Frutos & Fabra, 2012), on the availability of option contracts (Holmberg & Willems, 2015), as well as on arbitrage opportunities (Ito & Reguant, 2016). The paper closest to ours is Mahenc and Salanié (2004). They show that when products are differentiated and prices are strategic complements, producers can buy their production forward to soften spot market competition. We study a setup where firms sell a homogeneous product in multi‐unit uniform price auctions. In this context, “buying forward strategies” payoff even when firms do not alter market prices. In our analysis, financial contracts establish coordination on bidding strategies amid multiple equilibria on the spot market and effectively redistribute rents. This mechanism is similar to the one outlined in the industrial organization literature on side payments to enforce collusion (e.g., Harrington & Skrzypacz, 2007). In our case, financial contracts make side payments credible by conditioning payments on the market outcome. Our paper is also related to the empirical literature on strategic firms signing forward contracts (e.g., Hortacsu & Puller, 2008; van Eijkel, Kuper, & Moraga‐González, 2016; Wolak, 2003) or investing in new capacities (Grimm & Zoettl, 2013), before competing on the spot market. Moreover, Schwenen (2015) studies spot market bidding behavior in the New York power market from 2003 to 2008. He empirically investigates the optimality of bidding strategies for all participating firms. We look at a subset of his observation period, and add to this paper by studying how contracting changes the incentives to (not) volunteer for the two largest firms. Finally, this paper also relates to the game theory literature on coordination games, as in our case firms have to coordinate on a volunteer, and miscoordination is costly. In the laboratory, Goeree et al. (2017) show that miscoordination (e.g., the no‐volunteer outcome) increases with the number of players. Our model shows how contract payments contingent on the outcome of the game solve the volunteer's dilemma. 3 The next section characterizes the auction model and the resulting volunteer's dilemma. Section 3 characterizes conditions under which forward contracts solve this dilemma. Section 4 tests our theoretical predictions using a Monte Carlo simulation. Section 5 discusses model extensions to a broader set of market environments. Section 6 concludes. 2 | THE MARKET ENVIRONMENT We consider a standard multi‐unit uniform price procurement auction framework (e.g., Fabra et al., 2006) and derive necessary conditions for a volunteer's dilemma in bidding strategies. Two large and strategic firms i,j= 1, 2 with i≠j, and a competitive fringe participate in a multi‐unit uniform price auction. 4 Before bidding, the auctioneer publicly announces a demand function. In line with our empirical application we assume linear demand of Dp a dp()= − , (1) with market price pand constant parameters aand d. All firms have zero marginal costs. Each large firm ioffers a price‐quantity pair (b i ,k i ), where k i is the exogenous maximum quantity that firm iis willing to sell at or above an equilibrium auction price of b i . 5 The fringe acts as price‐ taker and therefore always submits its full capacity k f at marginal costs, that is, at prices of zero. The clearing price p* equates demand and supply. The auction clears with uniform pricing so that all bids below the clearing price win and receive the latter. To limit procurement costs, the auctioneer imposes a price cap p  . Bids are perfectly divisible. We further assume that both dominant firms are pivotal in clearing the auction at any positive price equal to or below the price cap. Assumption 1 (Pivotal firms and no rationing).For each large firm i= 1, 2 with ≠ i jDp k k,( )−−>0 fj and D (b i |b i =p*) ≤k f +k i +k j holds, where ∈ b pp=[0, ] * iis the optimal bid of the price‐setting firm i. 3 Boom (2008) uses equilibrium selection arguments to rule out multiple equilibria in multi‐unit auctions. Applying risk‐dominance criteria, it can be shown that larger firms set the clearing price. In a supply function equilibrium model, Hortaçsu, Luco, Puller, and Zhu (2019) reduce the number of equilibria using a Cognitive Hierarchy model. 4 The fringe supply is not needed for our main theoretical arguments. We add fringe firms to align the model to our empirical application. 5 The maximum quantity that firm iis willing to sell corresponds to its exogenously given installed capacity k i . The choice of submitted capacity, potentially smaller than k i , is not relevant for our main results. Also note that the assumption of discrete one‐step bid functions simplifies the exposition without changing the results. As shown by Fabra et al. (2006), the equilibrium clearing price is independent of the number of bid steps. Figure B4 graphs the auction outcome for one representative auction, May 2006, and shows that the assumption of discrete bids captures firm behavior in the market that we study reasonably well. LE COQ AND SCHWENEN | 243 Firm i's profits can be written as πqbbk p=(,,) , * iiijf (2) where firm i's quantity sold in the auction, q i (b i ,b j ,k f ), is defined as ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ q bbk kbbp k kk Dp k b b p Dp k k b p b (, , )= if < = +(()−)if == ()−− if = > . * ** ** iijf iij i ij fij fj i j (3) In case of bid ties the auctioneer rations supply at the margin pro rata. 6 2.1 | Volunteer's dilemma Given Assumption 1 and the allocation rule in (3), all firms but the price‐setting one sell their entire submitted capacity. The price‐setting bidder, in contrast, satisfies residual demand. Each firm hence prefers a market outcome in which its rival firm acts as price‐setter. Conversely, accepting the role of price‐setter is a best response if rivals choose against playing this role. Bidders consequently face a volunteer's dilemma (Diekmann, 1985), where one price‐setting bidder (the volunteer) is needed for all rivals to sell their submitted capacity at a favorably high price. However, volunteering is costly as bidders who price high and increase the clearing price on behalf of the market sell less as compared with undercutting their rival. Next, we characterize the volunteer's dilemma more formally. When firm ivolunteers to submit the clearing bid, so b i >b j , it optimizes against its residual demand and finds the optimal clearing bid b qbbk bp=min{argmax ( , , ) ,¯}, iV biijfi i (4) where the superscript Vdenotes the optimal bid of a firm that volunteers to clear the market. Firm ivolunteers if offering b iV is a more profitable strategy than undercutting its rival bid b j . Formally, this holds if ⋅ () ( ) πbbqb πbb bk=,>(<)= iiViViiVii j ji . This inequality is fulfilled if firm j, in turn, chooses a bid b j sufficiently low such that it is never optimal for firm ito undercut. This is the case if the free‐riding firm jsubmits any bid ∈ ⋅ () b bb bqb k [0, ¯)with¯= , , j Fjj iViiV i (5) where the superscript Fdenotes bids by any firm i,j= 1, 2 with i≠jthat free‐rides, becoming the inframarginal bidder and selling at full capacity. Depending on whether or not the price cap is binding, the volunteering firms' equilibrium profits become ⎧ ⎨ ⎪ ⎩ ⎪ () πb ak k dbp pDp k k b p = (−−) 4if < ¯, ¯(( ¯)−−)if = ¯. iiV fj iV fj iV 2 (6) The first part of the equation, when the price cap is not binding, corresponds to the profits associated with bid bp =<  iVak k d −− 2 fj as defined in Equation (4). The second part of the equation, when the price cap is binding, corresponds to the profits from selling residual demand of q i as defined in Equation (3) at a price equal to the cap. 6 Holmberg (2017) shows how alternative rationing rules impact auction outcomes. 244 | LE COQ AND SCHWENEN Due to the uniform price auction, the free‐riding firm isells all of its submitted quantity at the high price set by its rival and receives profits ⎧ ⎨ ⎪ ⎩ ⎪ () πb ak k dkbp pk b p = −− 2if < ¯, ¯if = ¯. iiF fi ij V ij V (7) Given that volunteering is the best response to a free‐riding rival, there are multiple equilibria that differ in the identity of the volunteering firm as well as the low bid offered by the free‐riding firm. The volunteer's dilemma arises because each firm always prefers that the other one volunteers and sets the clearing price. The volunteer's dilemma applies to a subset of existing equilibria described by Fabra et al. (2006) and de Frutos and Fabra (2012). In particular, for the dilemma to be relevant, the dominant firms must be sufficiently symmetric in capacities, as specified in Lemma 1. Lemma 1 (Sufficient symmetry).A volunteer's dilemma exists if the two pivotal firms are sufficiently symmetric such that ≤kkkk<ˆ( ) ijji where kk ˆ( ) ji satisfies πbbk πbk b(< ( ˆ)) > ( ( ) > ) jj iVjj j Vii with i = 1, 2 and i ≠j. Intuitively, Lemma 1 states that the relative capacities must be such that each firm prefers to be the inframarginal supplier. Hence kk ˆ( ) ji characterizes the maximum capacity of the largest firm jfor which the volunteer's dilemma still exists. The functional form of kk ˆ( ) ji follows from comparing firm j's profits from being inframarginal of πbbk(< () ) jj iVj with profits from volunteering of πbk b(()>) jj Vii . When the price cap is nonbinding, the condition in Lemma 1 becomes k> ak k dj ak k d −− 2 (−−) 4 fj fi 2. Equating and solving for k j yields the sufficient symmetry condition in Lemma 1. When the largest firm's capacity is above this threshold, the remaining demand and hence the clearing price set by its rival are so small that the larger firm prefers to clear the auction itself. As a result, the volunteer's dilemma vanishes. We derive kk ˆ( ) ji in detail in Appendix A.1. Note that kk ˆ( ) ji includes the case of binding price caps for both dominant firms. In this case, firm jyields profits pk j when free‐riding and pDp k k (( )−−) fi when volunteering. When price caps are binding, the only case where free‐ riding profits would not be larger is the case where kDp k k<( )−− jfi , which is ruled out by Assumption 1. Corollary 1. For any equilibrium ∀bpbb i ( =¯,< ¯)=1, 2 iVj Fj and i ≠j, the volunteer's dilemma exists. Hence if the price cap is the optimal bid independent of the identity of the price‐setting firm, the volunteer's dilemma must exist. Corollary 1 follows directly from Assumption 1, which rules out rationing demand. Demand rationing constitutes the only case where both firms could submit a bid equal to the cap without compromising on sales and hence without facing the volunteer's dilemma. 3 | FINANCIAL CONTRACTS AS COORDINATION DEVICE In this section we study how firms' financial positions impact the volunteer's dilemma. Specifically, we show that by signing forward contracts, firms are able to coordinate on the identity of the volunteering firm and avoid miscoordination at the auction stage. Contracts are financial, hence they specify payments and no physical delivery. 3.1 | Optimal bidding with contracts We study a standard forward contract with a forward price ∈pp[0, ] sand firm‐specific contract quantity s i . Contract payments are given by (p*−p s )s i . We assume that before interacting on the spot market, each large firm learns about its rival's position. With contracting, firm i's profits can be written as πqbbk p p p s=(,,) +( −). ** iiijf si(8) LE COQ AND SCHWENEN | 245 Following conventional notation, the quantity contracted forward, s i , is positive (negative) if firm iis a net buyer (seller) on the contract market. That is, for any positive s i , firm ireceives payments whenever the clearing price is above the strike price. Payments instead reverse if the clearing price is below the strike price. If s i is negative, payments flow in the opposite direction. Note that the case with negative s i where firms are selling ahead is also studied in Allaz and Vila (1993), Wolak (2003), Hortacsu and Puller (2008), and Green and Le Coq (2010), while Mahenc and Salanié (2004) analyze the case where firms buy forward in equilibrium. Given its contract position, the optimal clearing bid for a volunteering firm iis given by b qbbk b b p sp=min{argmax ( , , ) +( −), ¯} . iV biijfi i si i (9) When the price cap is nonbinding, Equation (9) yields an optimal clearing bid of ak k s d −−+ 2 fji , so the clearing bid b iV increases in s i . Given the uniform pricing format, free‐riding firms' profits thus also increase in s i . With a binding price cap however, positive forward positions of the price‐setting firm do not increase market prices or producer rent on the spot market. In the following subsection, we focus on the case that we study in our empirical analysis, that is, the case where the price cap is binding. Specifically, we show that by signing two offsetting forward contracts, firms can swap profits to establish coordination at the auction stage. We discuss nonbinding price caps in Section 5 and present a characterization of equilibrium bidding for this case in Appendix A.4. 3.2 | Coordination with contracts In this section, we first state a Lemma on our main result, that is, a firm can credibly commit to free‐ride by holding a critically large short position. We then introduce a Corollary to narrow down this commitment for the case of miscoordination profits of zero. To ensure coordination, contracts must rule out one of the two pure‐strategy equilibria bb ( ,) iVj F with i= 1, 2 and i≠j. Without loss of generality, we consider the case where firm jvolunteers given its contract position. Contracts, therefore, must rule out the equilibrium bb ( ,) iVj F . For this to be the case, the contract must ensure that firm i's best reply to firm jbidding low is to also bid low. Put differently, the contract renders free‐riding bids of firm junprofitable. If this condition is fulfilled, firm ican use its contract position to credibly commit to free‐ride. Formally, firm imust sign a contract such that () () πbb p ps πbb p ps,+( ¯−)< , +( −). * iiVj Fsii iFj Fsi (10) The left‐hand side of this inequality includes firm i's profits for bp = iVplus contract payments. The right‐hand side represents firm i's profits in case both firms submit low free‐riding bids, again plus contract payments. In the latter case, the market price p* is determined by bbmax{ , } iFj F . Rearranging the inequality yields ()() s πbb πbb pp <− ,−, ¯− . * i iiVj FiiFj F (11) Equation (11) states that for all contract positions of firm ibelow s i , the contract commits firm ito not volunteer, even if firm jprices aggressively and submits b j F. Note that for b i F and b j Fmultiple equilibria exist (see Equation 5). Thus different equilibrium outcomes for πbb(, ) iiFj F can occur and thus define different critical contract positions s i . However, it must hold that s i < 0 because by definition pp −> 0 *, and for the volunteer's dilemma to exist we have πbb πbb(,)−(,)>0 iiVj FiiFj F . We summarize this finding in the following Lemma. Lemma 2 (Critical contract position).Firm icommits to free‐ride by holding a short position. Specifically, firm i's critical contract position must satisfy s<−<0 i πbb πbb pp (,)−(,) ¯−* iiVj FiiFj F . 246 | LE COQ AND SCHWENEN The critical contract position s i in Lemma 2 is independent of the forward price. This is because the contract payments −p s s i occur in any case, that is, on both sides of Equation (10). However, the contract impacts profits at the auction stage via the difference between the forward price and the clearing price. Given firm i's contract position, firm j has an incentive to volunteer, and so the clearing price will be equal to the price cap. In turn, together with s i < 0 this implies total contract payments for firm iof pps ( −)<0 si. Put differently, firm ipays pps ( −) sifor incentivizing firm j to volunteer. Consequently, the commitment is costly to firm i. Equation (11) also shows that for a larger difference in volunteering and free‐riding profit, πbb πbb(,)−(,) iiVj FiiFj F, firm ialso has to increase its short position (further reduce s i ) to achieve commitment. The short position that yields commitment in all cases, that is for all outcomes for πbb(, ) iiFj F , is hence a contract that assumes b b==0 iFj F and, consequently, πbb(,)= 0 iiFj F. In this case, firm i's condition for credible commitment yields () πbb p ps ps,+( ¯−)<− . iiVj Fsisi(12) Using πbb pDp k k(,)= ¯(( ¯)−− ) iiVj Ffj , the critical contract position can be rearranged to sDpkk<−()+ + . ifj (13) Since by assumption dominant firms are pivotal, we again have s Dp k k<−()+ + <0 ifj . 7 We summarize this finding, that we test in our empirical application, by the following corollary. Corollary 2 (Sufficient contract position).Any short position of sDpkk<−(¯)+ + <0 * ifj is a sufficient contract position for firm i to commit to not volunteer. That is, this contract position suffices to implement commitment for all outcomes of πbb(, ) iiFj F . Lastly, note that the volunteering firm jcan sign an exactly offsetting contract s j =−s i . For any s j ≥0, firm j maximizes profit by bidding the price cap, because ∂ ∂> 0 b s j V j(see Equation 9). As a result, when firm jsigns an offsetting contract with s j =−s i , the two contracts together redistribute rents of pps ( −) sjfrom the free‐riding firm ito the price‐ setting firm j. Whether two offsetting contracts are beneficial to both dominant firms depends on counterfactual profits without the contract. In the empirical section, we use mixed‐strategy profits as a counterfactual and illustrate that contracts, as studied above, not only implement credible commitment but also increase payoffs for both contract parties. 4 | APPLICATION In this section, we employ a Monte Carlo simulation to test our model. We exploit data from the New York City power market as well as data from financial contracts signed by two dominant firms participating in this market. All data are available on the website of the New York independent electricity system operator (NYISO). 8 4.1 | Market institutions and data Our application makes use of data from the NYC procurement auctions for power‐generating capacity. For each calendar month, the NYISO procures the generating capacity needed to cover maximum electricity demand. The regulatory rationale for doing so is to secure sufficient generation capacity at all times to avoid black‐outs and rationing. To this end, the NYISO conducts a procurement auction and publicly announces a demand curve for available capacity. The demand curves are announced seasonally. The NYISO announces one winter demand curve that applies in six monthly auctions during a predefined “winter period”between November and April, and one summer demand curve 7 Appendix A.2 provides another argument why the critical contract position must be the largest for π bb(,)= 0 iiFj F . 8 The data that support the findings of this study are available at https://www.nyiso.com. LE COQ AND SCHWENEN | 247 for six monthly auctions in the “summer period”from May to October. Winning bidders receive a monthly payment for holding capacity available during the respective month. As generating units commit to be available one month ahead, opportunity costs for generation are limited, and marginal costs are near zero (Cramton & Stoft, 2005). We therefore disregard costs in our simulation. Capacity can be sold in sequential markets. The NYISO conducts forward procurement auctions and deducts all previously sold capacity from the demand in the final spot auction. As we lack sufficient data on the allocation of firm‐ specific capacity among the sequential markets, we abstract from sequentiality in our simulation and map the total firm capacities against total demand during the summer and winter periods. The two firms involved in the contract were two dominant firms in the market, Astoria and Keyspan. The contract payments started with procurement auctions for the summer 2006 season and were to last until 2009. The contract at stake specified payments for 1,800 MW. Based on this quantity, payments were determined by calculating the difference between the auction clearing price and a predefined strike price. Astoria, the inframarginal firm in the market, took a short position and is the low‐bidding firm iin our theoretical framework. Keyspan took the offsetting long position and is the volunteering firm j. The strike price differed marginally for either firm to guarantee a margin for the financial intermediary that acted as a counterparty for the two dominant firms. 9 In addition to information on the contract, the data comprise demand curve parameters and firm‐level capacities for the six major firms operating in the NYC power market. Capacities are scraped from the annual NYISO reports that list all installed generation capacity for the state of New York. Capacities are reported in terms of available capacity (“capability”). 10 Available capacity determines the amount of capacity that firms can offer to the procurement auction. Due to seasonal outages or maintenance patterns, available capacity is, like the demand curves, determined by season. For our model simulations, we use data from 2006, the first contracting year. Table 1 presents the data on demand as well as data on the capacities of Astoria, Keyspan, and the fringe firms operating in the NYC capacity market, both before and for the first year of the contract period. As apparent, the firm's capacities and the demand vary slightly from year to year and across seasons. The four fringe firms' capacities are aggregated. Astoria increased its capacity by around 600 MW in 2006, as shown by the differences from summer and winter 2005–2006, respectively. 11 The last column of Table 1 depicts demand at the price cap, as announced by the NYISO. Whereas procurement auctions clear monthly vis‐à‐vis seasonally defined demand curves, the granularity of our simulation is bound to information on the half‐yearly capacities in Table 1. This also forces us to apply a Monte Carlo simulation rather than pursuing regression methods. In contrast to the model with one common price cap, the NYISO capacity market features firm‐specific bid caps that differ marginally across firms. For Astoria, the bid caps are at $12.34 and $5.67 for summer and winter 2006, respectively. For Keyspan, the bid caps are at $12.71 and $5.84 for summer and winter 2006, respectively. For our simulations, we set the predefined forward price as specified in the contract, so at $7.57 for Keyspan and $7.07 for Astoria. The difference is the margin for the financial intermediary. To illustrate the difference to observed clearing prices, Figure B1 displays observed monthly market prices (equal to Keyspan's bid cap) and the forward prices for three seasons before and after the contract start date. Note that the price cap is below the forward price during winter months. This implies that payments in winter must flow reverse, that is, from the pivotal to the inframarginal firm. We, therefore, analyze swapped payments over the course of one full year, over both summer and winter markets combined. We thus capture the net effect of payments from the low‐bidding to the volunteering firm across seasons and for an entire year. 4.2 | Empirical strategy Our simulation strategy proceeds in three steps. First, we test whether there indeed exists a volunteer's dilemma in the absence of the contract. To do so, we test whether firms are pivotal and whether the price cap is binding for both firms (in line with Corollary 1). 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Financial contracts as coordination device. J Econ Manage Strat. 2020;29:241–259. https://doi.org/10.1111/jems.12340 LE COQ AND SCHWENEN | 255 APPENDIX A: PROOFS A.1 Sufficient symmetry The volunteer's dilemma exists if it is costly to volunteer but still a best response when the competing firm does not. It therefore suffices to show that volunteering profits are lower than nonvolunteering profits, but higher than profits when no firm volunteers. We start by deriving the first condition, that is, when volunteering profits are lower than free‐riding profits. Assume first that the price cap is nonbinding. If firm jvolunteers, it earns profit equal to ak k d (−−) 4 fi 2. If, now, firm i volunteers, and firm jdoes not, profits for firm jwould yield k ak k d j −− 2 fj . Volunteering profits are hence lower than nonvolunteering profits for all kkk ak akk ak k<ˆ()= 1 2(−+4(−)−(−)−2) , jji f fi f i 22 which follows from equating volunteering and nonvolunteering profits and solving for the critical k j . Assume now that the price cap is binding for firm jbut not for firm i. Everything is the same but the profits when firm jvolunteers (and firm idoes not) become pDp k k (( )−−) fi . The above inequality can be rewritten as follows: kkk ak ak dk kDpp<ˆ()= 1 2(−+(−)+8( + −(¯)) ¯) . jji f f f i 2 Note that if the price cap is binding for firm iwith k i <k j , it must also be binding for firm j. Hence we ignore the case where the price cap is only binding for firm i. If the price cap is binding for both firms, the volunteer's dilemma always exists. Finally, for the second condition, that profits in each case need to be lower than profits when no firm volunteers, consider the case where both firms free‐ride and set maximum bids b b= iFi . By construction of b  i as defined in Equation (5), it must always be beneficial for one firm to deviate and volunteer. A.2 Critical contract positions with πbb(, )= 0 II Fj F Below, we provide another argument that the contract with πbb(,)= 0 iiFj Fis the largest contract and implements commitment also for all πbb(,)>0 iiFj F. We start by recalling the critical contract quantity in Equation (11): ()() s πbb πbb pp <− ,−, ¯− . * i iiVj FiiFj F Any s i satisfying the above condition must be negative and hence the inframarginal firm is a net seller. Furthermore, the following argument shows that the sufficient contract with b b==0 iFj F of sDpkk=−(¯)+ + =− * ifj πbb p (,) ¯ iiVj F induces commitment also at any positive miscoordination price. Next, note that for any positive miscoordination price p p < * ,firmi's sales are at least Dp k k()−− fj . First, it will only sell more because for any p p < * we have Dp Dp()> (  ) *.Second,firmi may sell its entire capacity k i at the miscoordination price p*. Using these lowest miscoordination sales of Dp k k()−− fj ,we conclude that miscoordination profit must at least be Dp k k p ( ()−−) * fj . Applying this lower bound for miscoordination profit to Equation (11), the critical contract can be reduced to sDpkk<−<−(¯)+ + * i πbb πbb pp fj (,)−(,) ¯− * iiVj FiiFj F ,whichequals exactly the critical contract with b b==0 iFj F .Now,iffirmiindeed sells more and πbb Dp k kp(,)>(( ¯)−−) * iiFj Ffj ,the nominator of − πbb πbb pp (,)−(,) ¯− * iiVj FiiFj F must decrease, and with it the critical short position. Thus the critical contract quantity with πbb(,)= 0 iiFj Fsuffices for committing to free‐ride for any ≥πbb(,) 0 iiFj F. A.3 Mixed‐strategy profits Resolving Equation (14) with πbb(,)= 0 iiFj Fyields the following optimal mixed strategy, that is, probability of volunteering: 256 | LE COQ AND SCHWENEN () ()()() ρ πbb πbb πbb πbb = , ,+ ,−, . j iiVj F iiVj FiiFj ViiVj V We can then write firm i's mixed‐strategy profits as follows: () () () () ()() ()()() () ρρπbb ρπbb ρρπbb πbbπbb πbb πbb πbb ρπ bb ,+(1−),+(1−),= ,, ,+ ,−, =, . ij iiVj VjiiVj Fij iiFj ViiVj FiiFj V iiVj FiiFj ViiVj V jiiFj V With positive free‐riding bids ∀ b i>0 =1, 2 iF , the mixed‐strategy of firm jderives from () () () () ρ πbb ρπbb ρπ bb ρπbb,+(1−),= ,+(1−), , jiiVj VjiiVj FjiiFj VjiiFj F where the left‐(right‐)hand side represents profits when firm ivolunteers (free‐rides). Solving for firm j's probability to volunteer yields ()() ()()()() ρ πbb πbb πbb πbb πbb πbb = ,−, ,−,+ ,−, . j iiVj FiiFj F iiVj FiiFj FiiFj ViiVj V Equilibrium mixed‐strategy profit of firm ithen becomes ()() () () () () ()()()() ()()()() ρ ρπ bb ρπbb ρρπbb ρπbb πbbπbb πbbπbb πbb πbb πbb πbb ,+(1−),+(1−),+(1−), = ,,−,, ,−,−,+ , . ij iiVj VjiiVj Fij iiFj VjiiFj F iiVj ViiFj FiiVj FiiFj V iiFj FiiVj FiiFj ViiVj V The first derivative of this last expression with respect to πbb(, ) iiFj F is strictly negative. This implies that mixed‐strategy profits with πbb(,)= 0 iiFj Fconstitute an upper bound. A.4 Nonbinding price caps Consider the case where the price cap is nonbinding before contracting. Contracts in this case increase producer rent by increasing the clearing price: The price‐setting firm jincreases the clearing price to some b sbs(>0)> (=0) j Vjj Vj. The inframarginal firm iwrites a contract with −s j =s i < 0. When the forward price is set such that b sp(>0)> j Vj s , firm i transfers rents to firm jas compensation for reducing its sales. In contrast, firm iearns additional rents on its full inframarginal capacity (without reduced sales). Hence the contract transfers parts of these additional rents to firm j. Note that in this case the condition for a sufficiently large contract changes. Specifically, the condition that leads to Corollary 2. in the main text changes to ⎛ ⎝ ⎜⎞ ⎠ ⎟ kka s dsak k s dpps (+ −)− 4+(−−)+ 2−<− . fj i i fj i ss i 22 Rearranging yields sakk<−++ ifj LE COQ AND SCHWENEN | 257 asthesufficientcontractquantitythatguaranteesequilibriawherefirmjvolunteers. Note that in both cases with and without binding price caps, the optimal contract for any free‐riding firm implies that it sells forward its residual demand (residual demand at the price cap for binding price caps and residual demand at a price of zero when price caps do not bind). APPENDIX B FIGURE B1 Market prices and strike prices three seasons before and after contract start date. The respective strike prices are in dashed lines and signal the start date of the contract in May 2006 FIGURE B2 Optimal unconstrained clearing bids (box plot) and price cap (dashed line). The two upper box plots display the optimal clearing prices of Astoria against 2000 fringe draws using parameters from Summer 2006 (left) and Winter 2006 (right). The two box plots below refer to the corresponding optimal clearing bids of Keyspan 258 | LE COQ AND SCHWENEN FIGURE B3 The left panel shows the density of simulated optimal contract volumes as in Corollary 2. from 2000 fringe draws. The mean is equal to 1,821 MW, while the observed contract volume is 1,800 MW. The center and right panel show simulated profits for Astoria and Keyspan, respectively, for πbb(,)= 0 iiFj F. The solid distribution represents mixed‐strategy profit. The transparent distribution represents profits with the contract for Keyspan. For Astoria, profits with the contract are deterministic and represented by the solid vertical line. Profits are in million USD FIGURE B4 The Figure depicts the step‐wise nature of supply bids in the New York City capacity market. It shows supply bids and demand for May 2006. Demand is in black, all supply bids in blue. All capacity sold ahead of the spot auction (about 6,850 MW) is added at a bid of zero. The clearing bid is equal to the price cap of 12.71 USD. All capacity submitted at this price belongs to one firm ID LE COQ AND SCHWENEN | 259