Competition between Informed Venture Capitalists andEntrepreneurs’ Fund-Raising Strategy

Catherine Casamatta1 Carole Haritchabalet2

This version: june 2008

1Toulouse School of Economics (CRG, IDEI) and Europlace Institute of Finance2Toulouse School of Economics (GREMAQ).

Special thanks to Bruno Biais, Denis Gromb, Philippe Marcoul, Thomas Mariotti, Soren Bo Nielsen,Alexander Stomper, Elu von Thadden and participants to the 6th bundesbank spring conference onFinancing Innovation (2004), the Toulouse Finance Workshop (2004), the Econometric Society EuropeanMeeting (2004), the ASSET meeting (2004), the JMA (2006), and the second Vienna Symposium onAsset Management (2006).E-mail: catherine.casamatta@univ-tlse1.fr, carole.haritchabalet@univ-tlse1.fr. Corresponding address:Université de Toulouse I, 2 rue du Doyen-Gabriel-Marty 31042 Toulouse Cedex, France.

Abstract

This paper analyzes some determinants of profits and deal flows in the venture capital in-dustry. The model studies the problem of an entrepreneur who faces several investors with moreinformation about his project’s quality. We explore how the entrepreneur can optimally choosea fund raising strategy to maximize his expected utility. Importantly, we assume that the en-trepreneur derives a private benefit of control, so that he cares not only about expected monetaryprofits, but also about the probability to obtain financing. We show that if the entrepreneurenforces upfront competition by sending his project to all venture capitalists, he obtains highexpected monetary profits, but has a low probability to obtain financing. If he initiates negoti-ation with one venture capitalist, before enforcing competition, he can increase the probabilityto obtain financing, although the deal terms are less favorable. For low levels of private bene-fits, the model predicts that the venture capitalists’ deal flow is high, but that only experiencedventure capitalists make profits. For high levels of private benefits, expected profits increase forless experienced venture capitalists, and the deal flow and expected profits decrease for moreexperienced venture capital firms.Keywords: deal flow, asymmetric information competition, venture capital industry, fund raisingstrategy, informed investors.JEL codes: G2, G3, D8.

1 Introduction

Venture capital financing has been largely explored by the financial literature over the last decade.Many papers have stressed the difficulties faced by entrepreneurs who seek financing, arisingfrom project uncertainty, asymmetric information, and moral hazard. These papers generallyrationalize the use of specific contractual arrangements to cope with these issues (e.g. the useof convertible bonds or preferred stocks, the staging of investment, the syndication of deals. . . )In most of that literature, one entrepreneur is assumed to face either one, or a large numberof perfectly competitive investors. Little has been said on the workings of competition in theventure capital industry. What determines the deal flow of venture capitalists? What are theresulting profits for entrepreneurs and investors? The question is of interest in a context whereinvestment opportunities lie in private and unknown firms. Unless revealed by entrepreneurs,these potential deals are not known to investors. As a consequence, the effectively competinginvestors are those contacted by entrepreneurs. It turns out that the nature of competition is,at least partly, driven by the fund-raising strategy adopted by entrepreneurs. The focus of thispaper is on the determinants of the entrepreneurs’ fund-raising strategy. Our objective is toexplore how the specific features of start-up financing shape the nature of competition in theventure capital industry, affect the entrepreneurs’ ability to raise funds, and the investors’ dealflow and equilibrium profits.

Our analysis ultimately sheds light on the drivers of performance in the venture capitalindustry. Empirically, the performance of venture capital investments varies with whose per-formance is measured. One the one hand, entrepreneurs do not seem to earn large monetaryprofits. Moskowitz and Vissing-Jorgensen (2002) identify a private equity premium puzzle, byemphasizing the low expected returns earned by individual private equity owners (householdsand entrepreneurs). On the other hand, the gross returns of venture capital funds often outper-form the market index. Phalippou and Gottschlag (2007), Kaplan and Schoar (2005), Jones andRhodes-Kropf (2003), Ljungqvist and Richardson (2003), and Cochrane (2005) all document theoverperformance of private equity funds before fees.1. Note that these studies disagree on theperformance of the VC funds after fees. In our model, we do not consider venture capital fundsand investors as separate entities. Our analysis thus relates to the determinants of gross returnsonly.

Importantly, the performance across venture capital funds and industries varies. Kaplan andSchoar (2005) insist on the persistence of venture capital funds performance, suggesting that someventure capitalists are more skilled, experienced, or network-connected and capable of generating

1Cochrane (2005) however reports similar performance patterns for the smallest Nasdaq stocks, implying thatthese excess returns are not specific to private equity. The other studies usually compare the performance ofprivate equity funds with that of the market index, implicitly assuming that the risk profile of these investmentsis similar to that of the market.

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higher profits. Hsu (2004) confirms that high-reputation venture capitalists acquire start-upequity at a discount. The international comparative study of Hege, Palomino, and Schwienbacher(2006) documents that the US venture capital industry outperforms the EU industry. However,the same study reports that US venture capitalists do not outperform European funds wheninvesting in European projects. Apparently, experience or reputation is not a sufficient conditionto generate high returns. These aspects do change the way venture capitalists do their jobthough. Several international comparison studies report that venture capitalists do not behavethe same, nor use the same contractual agreements in different countries: Bottazzi, Da Rin, andHellmann (2005, 2007) find that more experienced venture capitalists, and venture capitalistsoperating in "better" legal systems are more actively involved in their portfolio firms. Cumming,Schmidt and Walz (2004) also document that legality impacts the investment policy and boardrepresentation of venture capitalists. Last, Kaplan, Martel, and Strömberg (2007) find less use ofconvertibles and contingent control components in European VC contracts. In the current paper,we want to investigate how experience or reputation determines venture capitalists’ behavior andprofits, as well as market conditions (i.e. the level of competition).

To study these issues, the paper relies on the premise that entrepreneurs, although able toconceive new and potentially profitable projects, are unable to know whether these projects arecommercially viable or not. By this assumption, we follow the literature that emphasizes thatentrepreneurs usually lack managerial knowledge.2 By contrast, venture capitalists have superiorability to obtain private information on the projects’ profitability.3 Quite plausibly, the precisionof their information depends on their individual level of experience. Possible explanations are thatventure capitalists acquire specific knowledge from their focus on industrial sectors, geographicalareas, or simply from repeated investments (see Gompers (1996), Hsu (2004) and Kaplan andSchoar (2005)). For a given entrepreneurial project, there are thus different types of venturecapitalists in the industry. Accounting for the dramatic growth of venture capital supply overthe last decade,4 we assume that entrepreneurs are able to generate offers from more than oneventure capitalist if they submit their project to several investors. This is consistent with Hsu(2004) who finds in his sample that about 1

3 of the start-up firms receive more than one offerfor their first-round investment. Last, we assume that entrepreneurs value monetary profits,and derive also private benefits from the realization of their projects. These private benefitscan reflect entrepreneurs’ satisfaction to see their idea developed, or simply their utility fromhaving the control of the firm. Alternatively, private benefits can stand for the level of future

2This assumption is shared by papers pointing out managerial skills uncertainty (Admati and Pfleiderer (1994)),or the need to obtain venture capital advising (Repullo and Suarez (2004), Schmidt (2003), or Casamatta (2003)).

3There is large empirical evidence that venture capitalists are able to obtain specific information on theirportfolio investments: see e.g. Sahlman (1988, 1990), Fenn, Liang and Prowse (1995), Gompers (1995), or Kaplanand Strömberg (2004).

4Venture capital investments in the US doubled in the last ten years, from $ 10.8 bn in 1996 to $ 22.3 bn in2005 (Source: NVCA).

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perquisites, or future incentive rents. They are then (inversely) related to the quality of thecorporate governance. The existence of non pecuniary benefits associated with entrepreneurialventures has been documented in a survey carried out by Blanchflower and Oswald (1992). In asimilar spirit, Hamilton (2000) and Moskowitz and Vissing-Jorgensen (2002) find low monetaryreturns on entrepreneurial investments, and interpret these results as evidence of the existenceof private benefits. As a consequence, entrepreneurs in our model care about their expectedmonetary returns, but also about their expected private benefits when considering their optimalfund raising strategy. In this context, an entrepreneur can either send his project to severalventure capital firms at the same time, thereby enforcing competition. Or, he can engage in anegotiation process with only one venture capitalist, postponing competition to a later stage.The contribution of the paper is to determine which of these two generic strategies will be chosenby the entrepreneur.

Our analysis delivers the following results. First, in the negotiation game, two equilibria canarise. In the first equilibrium, the entrepreneur accepts any offer at the negotiation stage, andhis expected utility is equal to his expected private benefit. This equilibrium is sustained bythe second venture capitalist’s belief that he is contacted only when the first venture capitalisthas received a low signal. If the initial offer is rejected, and competition is enforced, the secondventure capitalist therefore does not bid aggressively. This in turn undermines effective compe-tition. In the second equilibrium, the entrepreneur always rejects the first venture capitalist’soffer, and enforces competition. In this second equilibrium, the outcome of the negotiation gameis equivalent to the outcome of the initial competition game. However, this second equilibriumdoes not always exist because enforcing competition can be costly for the entrepreneur. First,it lowers the entrepreneur’s probability to obtain financing which reduces his expected utility.Hence, high levels of private benefit rule out this equilibrium. Second, the monetary profit thatcan be shared between the entrepreneur and the first venture capitalist at the negotiation stagecan be larger than what they jointly obtain if the entrepreneur enforces competition. When itis the case, the entrepreneur is more willing to accept an agreement at the negotiation stage,which destroys his threat to enforce competition. Consider next the upfront competition game.The equilibrium is then in mixed strategies (as was already emphasized by Broecker (1990),Hauswald and Marques (2003) and von Thadden (2004)). The heterogeneity among venturecapitalists determines the profits earned by the venture capital firms, as well as the probabilityto obtain funding. In particular, we show that the more experienced venture capitalist earnshigher expected profits. This is because an experienced venture capitalist suffers less from awinner’s curse and is able to bid more aggressively, which in turn increases the probability forthe entrepreneur to obtain financing.

Given the outcome of each game, we explore what is the optimal fund raising strategy ofthe entrepreneur. When the level of private benefit is low, the entrepreneur cares more about

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monetary profits, and prefers to enforce upfront competition. In this environment, each ven-ture capitalist’s deal flow is high (both receive an investment candidate to analyze), but onlythe more experienced venture capitalist is able to make positive profits. As the level of privatebenefits increases, the entrepreneur cares more about the probability to obtain financing. Inthat case, enforcing upfront competition can be costly. When venture capitalists have privateinformation about the project value, they compete under asymmetric information and face astandard winner’s curse problem. As a result, they bid less often than they would under sym-metric information. When the level of private benefits is large enough, the entrepreneur favorsnegotiation and sends his project to the less experienced venture capitalist first. As a conse-quence, the deal flow of the experienced venture capitalist shrinks (because he receives only thedeals that have been rejected by the first venture capitalist), and so does his expected profit.At the opposite, the profit of the less experienced venture capitalist increases compared to hislevel in the upfront competition game. These results also allow to explore the decision of ven-ture capitalists to syndicate their investments. The profits earned by each venture capitalist inthe competition game determine their reservation utility when deciding whether to syndicate ornot. If the entrepreneur enforces upfront competition, the more experienced venture capitalistis more reluctant to syndicate, since he can secure positive expected profits when competitiontakes place. Also, having a superior signal, he does not gain much from sharing information. Inthe negotiation game, because he earns positive expected profits, the less experienced venturecapitalist is also not very keen to undertake syndication. Overall, we find that syndication ismore likely when venture capitalists are more alike, which is in line with the results of Lerner(1994).

According to the level of private benefit of the entrepreneur, our model predicts that differentcompetition regimes emerge. This affects both the efficiency of the venture capital investments,as well as the relative profits across funds in the industry. We are able to derive the followingempirical predictions. If one interprets the level of private benefits as the future resources that willbe diverted by entrepreneurs, one implication of the model is that venture capital investments aremore profitable the better the corporate governance. This result is consistent with the empiricalevidence that the performance of the venture capital industry differs across countries (e.g. Hegeet al. (2006)). Also, when comparing the profits on investment of each VC fund, we find thattheir relative performance depends on the nature of competition. Specifically, when competitionis effectively intense, more experienced VCs perform better than less experienced VCs: this is inline with the findings of Kaplan and Schoar (2005). However, this needs not be the case when theentrepreneur favors negotiation. In that case, experienced VCs can outperform or underperformless experienced VCs. This can explain why although the US venture capital industry performsbetter than its European counterpart, US funds do not earn higher profits than European oneswhen investing in Europe. When the nature of competition changes, the ability of experiencedVCs to earn profits changes also.

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Our paper is directly linked to the literature on competition between financial intermediarieswith asymmetric information. This topic has been initiated in the banking literature by Broecker(1990), Sharpe (1990) (see also von Thadden (2004) for a restatement of Sharpe’s problem) andRajan (1992) who study competition between asymetrically informed banks. In the context ofupfront competition, Hauswald and Marques (2003) investigate what are the incentives of insidebanks to exert effort to collect costly information. Thakor (1996) focuses on the optimal numberof banks approached by firms in a simultaneous competition game. Other papers study situationsof informed investors and focus on the optimal contract design: Inderst and Mueller (2006) andPeyrache and Quesada (2006) mainly study the case of a monopolistic informed investor, whileAxelson (2007) and Garmaise (2006) study competition. In contrast to those papers, we abstractfrom the issue of optimal contract design,5 and we endogenize the nature of the competition game:by studying the optimal fund raising strategy of entrepreneurs, we explicitly determine whetherinvestors face competitors when making offers.6 This question is particularly relevant in theventure capital context where new investment opportunities cannot be easily spotted by venturecapitalists. We explicitly account for the private nature of these investments, and we highlightsome determinants of the venture capital firms’ deal flow, and level of profits.

Our analysis also shares ideas with the papers of Anton and Yao (1994), and Berkovitch andKhanna (1991). Anton and Yao (1994) explore how an entrepreneur can use the threat of compe-tition to extract innovation rents. However, they investigate how an informed entrepreneur canconvey his information without being expropriated. We consider an uninformed entrepreneur,and show that asymmetric information across investors alters competition. Berkovitch andKhanna (1991) study the optimal acquisition mechanism between a merger and a tender of-fer. The main difference with our analysis is that tender offers can lead to competition becausethey are publicly observed. In our model, offers cannot be observed publicly, which leads toasymmetric information competition.

Last, our model is related to the literature on venture capital financing. A major differenceis that while a large body of that literature has emphasized the monitoring and value-addedactivities of venture capitalists, 7 and studied the financial contracts between venture capitalists

5We do consider optimal contracts, but our specification of the distribution of returns simplifies this issue.6Broecker (1990) compares the equilibrium outcomes of a one-stage and a two-stage game. However, the two-

stage game he considers is different from our bilateral negotiation game. In his model, banks make competitivebids at the initial stage, and can leave the market at the second stage after observing competitors’ bids. This isnot relevant in our setting where offers cannot be observed. In our bilateral negotiation game, an investor has theopportunity to offer a bid before competition takes place. This allows the two investors to make positive profits,which does not happen in the two-stage game considered by Broecker (1990).

7See Admati and Pfleiderer (1994), Bergemann and Hege (1998), Cornelli and Yosha (2003), and Dessì (2005)for a theoretical analysis of sequential investment and the optimal continuation decision, Schmidt (2003), Renucci(2006), Repullo and Suarez (2004), or Casamatta (2003) on the advising role of venture capitalists, and Chan,Siegel and Thakor (1990), Hellmann (1998) or Cestone (2002) on the control exerted by venture capitalists.

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and entrepreneurs,8 we emphasize their screening role. We also depart from models that assumeprivate information on the entrepreneur’s side (e.g. Cornelli and Yosha (2003), Ueda (2004),or Dessì (2005)), since we assume that investors have superior information due to their duediligence process. The fact that some venture capitalists are more experienced than others hasalso been largely documented. Papers have explored the importance of the level of experienceof venture capitalists to determine the decision to syndicate (Lerner (1994), Hopp and Rieder(2006), Casamatta and Haritchabalet (2007), Cestone, Lerner, and White (2006)), the value-added activities (Sapienza, Manigart, and Wermeir (1996)), or the decision to exit (Gompers(1996)), but not to understand the nature of competition in the industry.

The paper is organized as follows. Section 2 presents the model and describes the timingof the games. Section 3 studies the outcome of the initial competition game between venturecapitalists. Section 4 derives the equilibria of the negotiation game. Section 5 studies the optimalchoice of the entrepreneur between competition and negotiation, and explores the levels of profitand financing patterns of the venture capital industry. Empirical implications of our theoreticalresults are explored in section 6, while section 7 extends the analysis to the syndication decisionof venture capitalists. Section 8 concludes and proofs are provided in the appendix.

2 The model

Investment project and returns

We consider a standard corporate finance model. An entrepreneur is endowed with a one-period innovative investment project. Innovative projects generally entail high potential returns,together with a high level of uncertainty. To capture these features, we assume that the projecthas the following characteristics.

First, the project return is risky. For simplicity, future cash-flows can take two values,depending on the state of nature. In case of success, the project generates a cash-flow R > 0,while in case of failure, the project generates a cash-flow 0. The probability of success dependson the quality of the project. Projects can be of two quality types: either good or bad. If theproject is good, success occurs with probability p. If the project is bad, the probability of successis lower. To lighten algebraic expressions, and because it does not impact our analysis, assumethat the probability of success of a bad project is zero. Last, the project requires an initial outlay,denoted I.

Second, there is some uncertainty regarding the true quality of the project. Initially, nobodyknows the project’s quality, and the prior belief that the project is good is denoted q0: this

8See Kaplan and Strömberg (2003) for a detailed empirical analysis of venture capital contracts.

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probability is common knowledge (i.e. all agents in the model have the same prior). To fitthe situation of early-stage financing, we consider that the project is very unlikely to succeed.Formally, we assume that the initial NPV of the project is negative, although the project isprofitable if it turns out to be of good quality. Assuming risk-neutral agents, and normalizingthe riskless interest rate to zero, this implies:

q0pR < I < pR.

The venture capital industry

The entrepreneur is cash-poor, and must raise funds from investors. Given the initial negativevalue of the project, he cannot raise funds from traditional investors, and must turn to specializedinvestors, i.e. venture capitalists (denoted hereafter VCs). Because of their repeated interactionswith entrepreneurs, and because of their experience at financing early stage ventures, VCs areable to (imperfectly) infer the quality of new projects.9 Technically, we assume that VCs performinvestment analyses and obtain at no cost a signal related to the project’s true quality.10 Thissignal can be either high (s = H) or low (s = L) and is all the more precise that the venturecapitalist’s expertise (or experience) is high. Formally, the signal s received by a venture capitalistwith expertise α has the following properties:

p(s = H/good) = p(s = L/bad) = α,

where α > 12 . After observing a signal, VCs update their belief on the project quality using

Bayes’ rule. We denote q(sα), the posterior probability that the quality of the project is goodgiven that a VC with experience α has received a signal s (s ∈ {H,L}). Assume that any VC issufficiently experienced so that his appraisal of the project becomes positive if he receives a highsignal. This means that:

α > αmin,

where αmin is defined by: NPV (q(Hαmin)) = 0.

The industry is heterogeneous, with some VCs of type α and some VCs of type α < α. Thisassumption captures realistic features of the industry, where some well-known and reputableventure capital funds compete with newer, less established funds.11 For simplicity, assume thatthere are two VCs in the economy, one being more experienced than the other. The project’s

9See Kaplan and Strömberg (2004) for a thorough analysis of the informational content of VC investmentmemoranda.

10Introducing a costly signal does not qualitatively modify the result of the upfront competition game: seeHauswald and Marques (2003).

11For sake of completeness, one could also consider the case of an industry where all VCs have the same levelof -high or low- experience. These cases do not add significant insights to the analysis, but considerably burdenthe presentation. The results are nevertheless available upon request.

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NPV depends on the relative precision of the two signals. To focus on the most interesting case,we assume that if the more experienced VC receives a high signal, the project NPV is positiveeven if the less experienced VC receives a low signal:12

NPV (q(Hα, Lα)) > 0 > NPV (q(Hα, Lα)). (1)

Entrepreneur’s utility

The entrepreneur derives utility from any financial return he receives from his firm, and alsofrom the mere fact of running a successful firm. We thus assume that he enjoys a private benefitB, if the project succeeds. This assumption is in line with the literature on entrepreneurship,which considers the satisfaction derived from being an entrepreneur as one of the determinants ofentrepreneurship. Blanchflower and Oswald (1992) document from survey data the existence ofnon pecuniary benefits in entrepreneurship. In a similar spirit, Hamilton (2000) and Moskowitzand Vissing-Jorgensen (2002) find low monetary returns on entrepreneurial investments, andinterpret these results as evidence of the existence of private benefits. In our setting, the privatebenefit is only enjoyed in case of success. This can reflect a possible "stigma of failure" incurredby entrepreneurs who do not succeed (see Landier (2005)), or simply the fact that private benefitsstand for future cash-flows and perquisites enjoyed by the entrepreneur if the firm goes on. Quiteplausibly these expected future benefits are zero if the firm fails.13 Therefore the utility of theentrepreneur can be written:{

UE = RE + B, in case of success,UE = 0, in case of failure,

where RE denotes the fraction of cash-flows attributed to the entrepreneur when the projectgenerates a cash-flows R. Note that we implicitly assume that the entrepreneur obtains nomonetary benefit if the project fails. It is however conceivable that VCs promise the entrepreneura positive reward even when the cash-flow is zero. Our analysis is immune to this: our results gothrough if one allows for more general distributions of monetary benefits for the entrepreneur.This is because the entrepreneur only considers his expected utility when he receives an offer. Aslong as the distribution of monetary benefits offered by the VCs does not affect the probabilityto obtain financing, the entrepreneur does not prefer one contract over an other (if contractsdeliver the same expected return). This is the case in our framework where venture capitalists’deals are binding. The project is financed with probability one, if the entrepreneur accepts thedeal.

12If this is not true, the results are similar to those obtained when VCs have the same level of experience.13In a previous specification of the model, we assumed that the entrepreneur’s private benefit was enjoyed

whatever the success of the firm: the current assumption does not modify qualitatively the results.

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First-best investment policy and fund-raising strategies

We first determine what is the optimal investment policy, i.e. the investment policy that max-imizes the sum of the venture capitalists’ and entrepreneur’s expected utilities. The latter isequal to the social NPV if the project. To make things interesting we assume that condition (1)still holds when considering the social NPV:

NPV (q(Hα, Lα)) + q(Hα, Lα)pB > 0 > NPV (q(Hα, Lα)) + q(Hα, Lα)pB. (2)

Conditions (1) and (2) imply that when the less experienced VC has received a high signal,but the more experienced VC has not, both the monetary and the social NPVs are negative. Asa consequence, the first best investment policy is to invest if and only if the more experiencedVC has received a high signal. We study below what investment policy can be achieved whensignals are privately observed by VCs.

The entrepreneur initially chooses a fund raising strategy, to maximize his expected utility.Given our assumptions, there are two relevant fund raising strategies: either the entrepreneursends his project proposal simultaneously to all potential investors, or he first sends his projectto one VC, postponing competition to a later stage. We assume that in each game, venturecapitalists do not observe competing offers. This assumption is in line with the practice ofthe industry, where venture capitalists, if contacted, may know whether competitors have beenapproached by entrepreneurs, but do not share information on their offers (unless they agree ona formal syndication deal: see section 7). The game is solved backward: for each fund raisingstrategy chosen by the entrepreneur, we determine the optimal response of venture capitalists (i.e.whether they accept to finance the venture, and at which financial terms). We then determine thefund raising strategy that maximizes the entrepreneur’s utility. One key determinant of the VCs’offers is whether a competitor has been contacted at the same time. However, we do not assumethat venture capitalists observe whether a competitor has been contacted or not. Instead, venturecapitalists anticipate which game is being played, from the equilibrium fund raising strategy ofthe entrepreneur. In other words, endogenizing the entrepreneur’s fund raising strategy allowsto relax the assumption that VCs observe whether they face a competitor.14 The possible fundraising strategies are generically denoted "upfront competition", when the entrepreneur contactsthe two VCs at the same time, and "negotiation", when he first contacts one VC only. In thelatter case, the entrepreneur further has to choose which VC to contact first.

14Therefore, our focus on the fund raising strategy of the entrepreneur rationalizes the standard assumptionin the literature on bank competition that banks know they are in competition: see Broecker (1990), Hauswaldand Marques (2003) or Thakor (1996). This assumption is not straightforward, in particular in a venture capitalsetting, because entrepreneurial ventures are private, and not easily spotted by VCs unless entrepreneurs applyfor financing.

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If the entrepreneur adopts the "upfront competition" strategy, the timing and assumptionsare as follows:

1. The entrepreneur proposes his investment project to each venture capitalist.

2. Each VC performs an investment analysis, obtains a signal si, and updates his belief onthe project’s quality. Each signal si is private information for V Ci.

3. Each venture capitalist proposes (or not) a financial contract to the entrepreneur. Whetheran offer is made or not, cannot be observed by competitors. A fortiori, the content of theoffer is not observable.

4. The entrepreneur chooses (if any) the offer that gives him the highest expected utility. Theninvestment takes place, revenues are realized, and are shared according to the contractualarrangement.

If the entrepreneur initiates negotiation with one VC, the timing is as follows.

1. The entrepreneur proposes his investment project to a first venture capitalist (denotedV C1).

2. V C1 performs an investment analysis, obtains a signal s1, and updates his belief on theproject’s quality. The signal is private information for V C1.

3. V C1 proposes (or not) a financial contract to the entrepreneur. If an offer is made, andthe entrepreneur accepts the contract, investment takes place, and revenues are realized.

4. If the entrepreneur rejects V C1’s offer, or if no offer has been made, the entrepreneur cancontact another VC, called V C2, who privately observes a signal s2 on the project’s quality.As before, V C2 does not know whether a previous offer was made or not.

5. V C1 and V C2 can propose a financial contract to the entrepreneur.15 The latter choosesthe bid that gives him the highest expected utility. In this case, because financing ispostponed, we assume that the entrepreneur’s utility is reduced by ξ > 0.

We solve the model backward, and first determine what are the outcomes of the upfrontcompetition game (section 3) and of the negotiation game (section 4). We then determine whatis the optimal strategy to maximize the entrepreneur’s expected utility (section 5).

15In that case, the first venture capitalist is able to modify his initial offer. This assumption is meant to fit theplausible feature that once an offer has been rejected, it is not binding any more.

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3 Upfront competition

Suppose that the entrepreneur chooses the upfront competition game. Then the two VCscompete under asymmetric information to finance the entrepreneur. After observing his signal,each VC has to choose whether to make an offer, and which financial contract to offer to theentrepreneur. In our setting where investment is binary and where the final payoff of the projectis either R or 0, the choice of the financial contract reduces to only one parameter γ, whichrepresents the fraction of the firm’s equity kept by the venture capitalist in exchange for hisinvestment I.16 Alternatively, this financial contract measures the post money value I

γ proposedby a VC. VCs privately observe their signal, and make simultaneous competing bids: γi andγj . The pure-strategy space is Γi = [0, 1] ∪ ∅ , the strategy ∅ means that V Ci does not makeany offer. The entrepreneur infers the informational content of each bid, and chooses the bidthat grants him the highest expected utility. The entrepreneur’s expected utility depends i) onthe probability that the project is good and succeeds, and ii) on his monetary reward givensuccess. Clearly, his optimal choice is then: min[γi; γj ]. Intuitively, once offers are made, thechoice between one offer and the other does not modify the informational content of the offers(i.e. the probability that the project is good given the offers). The entrepreneur then choosesthe offer that grants him the highest fraction of earnings, or the highest valuation bid.

We now characterize the equilibrium strategies of the VCs. Recall that each VC privatelyobserves his signal on the project’s quality. We consider the Nash equilibrium of the simultaneousbid game, where V Ci chooses a bidding strategy γi(s), taking into account his own signal, andthe equilibrium strategy γ∗

j (s) of V Cj .

Proposition 1 The equilibrium of the asymmetric information competition between the two VCsis unique and has the following properties.

When V Cα receives a high signal, with probability x, he randomizes according to the contin-uous distribution F (γ) on [γ̂α, 1] and, with probability (1− x), he plays γ∗

α = 1.

When V Cα receives a high signal, with probability x, he randomizes according to the contin-uous distribution F (γ) on [γ̂α, 1] and, with probability (1− x) he does not participate.

Last, each V C does not make any offer after observing a low signal.

The expected profit of V Cα is strictly positive and equal to I( q(Hα)q(Hα) − 1). The expected profit

of V Cα is equal to zero.

16As mentioned earlier, one can think of more general contracts, whereby the entrepreneur gets a positivemonetary pay-off in case of failure. This does not modify the results, since only the expected profit matters forthe entrepreneur. We thus abstract from the design of the financial contract bid, which is studied in Garmaise(2006), and which has no bite here.

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The functions F , F , the constants x, x,and γ̂α are defined in the appendix.

The result that no pure strategy equilibrium exists is standard in this type of asymmetricinformation auction setting (see Milgrom and Weber (1983), von Thadden (2004) and Hauswaldand Marquez (2003)). Note that the support of the mixed strategies, as well as the expectedprofits that VCs obtain in this competition game, depend on the level of experience of the VCs.The more experienced VC knows that the project has a positive NPV if he observes a high signal.He consequently always wants to make an offer. Of course, his profit is not very large when hiscompetitor has received a low signal. To compensate this winner’s curse, he must win sufficientlyoften when his competitor has received a high signal. This is the case if the less experiencedVC sometimes forgoes to participate even after a high signal. By definition of a mixed strategyequilibrium, a player must obtain the same level of profit for each strategy he can choose. Asa result, the less experienced VC obtains zero expected profits. For the same reason, the moreexperienced VC is able to earn strictly positive profits.

Corollary 1 There is overinvestment in the upfront competition game.

Corollary 1 states an important implication of the equilibrium in the upfront competitiongame. The proof is the following. In our information setting, the optimal investment policyis to finance projects if and only if the more experienced VC has received a high signal. Inthe equilibrium described in proposition 1, the more experienced VC always proposes a deal tothe entrepreneur if he receives a high signal. As a consequence, all positive NPV projects arefinanced. However, the less experienced VC sometimes makes an offer, and finances the project,if he receives a high signal and his competitor receives a low signal: this happens with probabilityprobLα,Hαx, where probLi,Hj denotes the probability that V Ci receives a low signal, and V Cj

receives a high signal. Therefore, some negative NPV projects are accepted, and the industryexhibits overinvestment. The next section explores what can be achieved if the entrepreneurdecides to negotiate with one VC before enforcing competition.

4 Negotiation

We now investigate the outcome of the negotiation game. Note that after choosing thisfund-raising strategy, the entrepreneur further has to decide which VC to start negotiating with.Again, we solve the problem backward and determine first what are the equilibrium outcomes ofinitiating negotiation with each VC.

To solve the game described in section 2, we look for a perfect Bayesian equilibrium (PBE)in which at each stage of the game, the strategies chosen by each agent are optimal given their

12

beliefs, and the beliefs are computed from these equilibrium strategies using Bayes’ rule. A keyelement for the competition threat to be effective, is that V C2 assigns a positive probability tothe event that V C1 has received a high signal, if the game gets to the competition stage. Thiscan only happen if either V C1 does not propose an investment contract to the entrepreneur aftera high signal, or if the entrepreneur rejects the investment contract proposed by V C1.

The next propositions present the characteristics of the different PBE of the negotiationgame.

Proposition 2 There always exists an equilibrium such that V C1 makes a monopoly offer to theentrepreneur when he receives a high signal, and such that the entrepreneur accepts the offer, i.e.does not enforce competition. In this equilibrium, the entrepreneur obtains zero monetary profit.

The intuition of proposition 2 is the following. Suppose that V C2 believes that he is contactedonly when V C1 has received a low signal. In that case, V C2 believes that he faces no competingbid if he makes an offer. As a consequence, his best response is to make a monopoly offer ifNPV (q(L1,H2)) > 0, and to make no offer otherwise. In both cases, the entrepreneur obtains(almost) zero monetary profit if he reaches the competition stage. Therefore, V C1 optimallyoffers a contract in which he captures the whole project surplus when he receives a high signal.The entrepreneur accepts this contract, since he does not obtain a higher utility when refusing.His utility amounts then to the level of his expected private benefit.

Proposition 3 When the entrepreneur contacts the less experienced VC first, there sometimesexists a second equilibrium of the negotiation game in which the entrepreneur makes positivemonetary profits. In this equilibrium, the entrepreneur always rejects V C1’s offer, and competi-tion always takes place. The conditions under which this equilibrium exists are provided in theappendix.

A consequence of proposition 3 is that the entrepreneur cannot obtain positive monetaryprofits when negotiating with one VC only. The only way for him to ensure positive monetaryprofits is to always enforce competition. In that case, the outcome of the negotiation game issimilar to the outcome of the initial competition game. In other words, the entrepreneur cannotuse the threat of competition to get some bargaining power at the negotiation stage.

The key point of the analysis is that when V C1 makes an offer, the entrepreneur knows thats1 = H. If competition is enforced, this is precisely the state of nature in which a positive profitmust be left to V C2 to counterbalance his loss when he finances a project and s1 = L. Thislowers the entrepreneur and V C1’s expected profits under competition, and makes them morewilling to negotiate ex ante. If their continuation profit is smaller than their joint negotiationprofit, V C1 can propose to the entrepreneur a slightly higher expected utility than what the

13

latter obtains under competition. In equilibrium, the entrepreneur does not enforce competitionwhen he receives such an offer from V C1, and the competition threat is not effective. But inthat case, V C1 optimally makes an offer that allows him to extract the whole monetary surplus.Therefore, the equilibrium in which the entrepreneur enforces competition does not always exist.

A crucial element for the equilibrium described in proposition 3 to exist is that the jointprofit of the entrepreneur and of V C1 is higher at the competition stage than at the negotiationstage. This can happen when the second signal adds value to the project. Indeed, if competitionis enforced, the first VC does not bid all the time (because he is less experienced), and somenegative NPV projects are not financed, while they would be at the negotiation stage. This alsoexplains why this equilibrium does not exist if the entrepreneur contacts the more experiencedVC first: if competition eventually takes place, the latter never refrains from bidding. Finally,note that this equilibrium is less likely when the entrepreneur’s private benefit increases. Indeed,if the entrepreneur rejects the initial offer and enforces competition, he lowers the probability toobtain financing, and thus his expected private benefit.

If the joint competition profits are higher than what the entrepreneur and V C1 obtain undernegotiation, any offer from V C1 is rejected by the entrepreneur, who enforces competition withprobability one.17 An interesting feature of this equilibrium is that the entrepreneur may endup accepting an offer that is strictly worse than the one he rejected. Thus, this equilibrium isconsistent with the empirical evidence provided by Hsu (2004), who finds that start-ups do notnecessarily accept the highest valuation deal. He explains this feature by the certification roleof VCs, pointing out the fact that entrepreneurs value being financed by a more reputable VC,while we emphasize specific patterns of competition between asymmetrically informed VCs.

Last, these results state that, in some situations, the entrepreneur is unable to derive bar-gaining power from the threat of competition, and to obtain a higher valuation for this project.Because competition between VCs is plagued by asymmetric information, the entrepreneur ishurt if he chooses to enforce competition rather than to negotiate. The reason is that whenthe entrepreneur infers that the first signal is high, he internalizes the consequence of the sec-ond VC’s winner’s curse if he enforces competition, which annihilates the threat of competition.When the second signal is much more precise than the first, this cost of enforcing competitioncan be outweighed by the benefit of obtaining the second signal, and competition can occur inequilibrium.

We conclude this section by exploring the efficiency of the investment decision in the negoti-ation game.

17Note that there might exist equilibria in which either V C1 makes the same offer whatever his signal, or makesno offer, and the entrepreneur enforces competition with probability one. Again, for such equilibria to exist, itmust be the case that the surplus that can be shared by V C1 and the entrepreneur at the negotiation stage islower than their joint expected profit if competition takes place.

14

Corollary 2 If the entrepreneur contacts the more experienced VC first, investment is efficient.If the entrepreneur contacts the less experienced VC first, there is overinvestment.

Corollary 2 follows directly from the result stated in proposition 2. If the entrepreneurcontacts the more experienced VC first, his project is financed each time V C1 receives a highsignal, and not otherwise. This is clearly the optimal investment strategy. If the entrepreneurcontacts the less experienced VC first, all positive NPV projects are financed, but also somenegative NPV projects: projects obtain financing when s1 = Hα, or when s1 = Lα and s2 = Hα.Straightforward computation show that :

probHα + probHα,Lα = probHα + probHα,Lα .

There is thus overinvestment when the entrepreneur contacts the less experienced VC first,and the expected profit in the industry is lower. In spite of the superior efficiency of initiatingnegotiation with the more experienced VC, this fund-raising strategy is strictly dominated fromthe entrepreneur’s point of view, as will be shown in the next section. The reason is that althoughthe social NPV is higher, the entrepreneur captures only part of it. Because he can only capturehis expected private benefit, the entrepreneur cares about the probability to obtain financing.

5 Entrepreneur’s optimal fund raising strategy

In this section, we analyze which fund raising strategy is chosen by the entrepreneur inequilibrium. To do this, we compare the entrepreneur’s expected utility when he initiates upfrontcompetition, and when he decides to negotiate first with one VC.

We need to determine which VC is contacted first by the entrepreneur, if he decides to initiatenegotiation.

Proposition 4 If the entrepreneur decides to negotiate, he always sends his project to the lessexperienced VC first.

The proof of proposition 4 is the following. Recall that in the equilibrium presented in propo-sition 2, the entrepreneur obtains zero expected monetary profits, because at each stage, onlyone VC makes an offer, and extracts all the project monetary surplus. To maximize his expectedutility, the entrepreneur simply chooses the strategy that grants him the highest expected privatebenefit. If he contacts the more experienced VC first, he obtains financing only if the latter re-ceives a high signal. Indeed, if the competition stage is reached, the second VC does not proposeany deal. His expected utility is then:

E(UE) = probHαq(Hα)B.

15

If the entrepreneur contacts the less experienced VC first, he obtains financing if the latterreceives a high signal, or if the second VC receives a high signal. His expected utility is therefore:

E(UE) = (probHαq(Hα) + probHα,Lαq(Hα, Lα))B − probHα,Lαξ,

= (probHαq(Hα) + probHα,Lαq(Hα, Lα))B − probHα,Lαξ,

which is clearly higher for low values of ξ. Finally, note that if the entrepreneur contacts theless experienced VC first, there can also exist an equilibrium in which the initial offer is rejected,and competition is always enforced. If the entrepreneur obtains a higher expected utility underthat equilibrium, he a fortiori contacts the less experienced VC first.

The following proposition now describes the optimal fund-raising strategy of the entrepreneur.

Proposition 5 If the level of private benefit B is sufficiently low, in the sense that:

B ≤

[probHα

(q(Hα)pR− q(Hα)

q(Hα)I)

+ probLα,Hαx(q(Lα,Hα)pR− I) + probLα,Hαξ]

(1− x)probLα,Hαq(Lα,Hα)(3)

the entrepreneur initiates upfront competition. Otherwise, he prefers to start negotiating with theless experienced VC.

Proposition 5 implies that when the entrepreneur values mostly monetary profits, he alwayschooses to enforce competition initially. Recall from the equilibria derived in sections 3 and 4that the entrepreneur cannot obtain more than the competition profits in the negotiation game.Therefore, the entrepreneur is always better off sending his project to the whole VC industry.

Importantly, entrepreneurs do not always have an interest to "flood the market" with theirinvestment projects. As mentioned previously, enforcing upfront competition is also potentiallycostly. Because of the winner’s curse, the less experienced VC refrains from making an offereach time he receives a high signal. Consequently, the probability of obtaining financing isdifferent in the two fund-raising strategies. When the entrepreneur derives a sufficiently highlevel of private benefit from implementing his project, he favors the negotiation strategy, eventhough his monetary profits are lower. Indeed, if the entrepreneur starts negotiating with theless experienced VC first, the probability to obtain financing is strictly larger than under upfrontcompetition: the entrepreneur obtains financing each time any of the two VCs has received ahigh signal. If the entrepreneur enforces upfront competition, this is not the case anymore, sincethe less experienced VC does not always make an offer after a high signal. Therefore, negotiationcan dominate competition.

The optimal fund-raising strategy of the entrepreneur obviously has consequences for the VCindustry. In particular, it affects the deal flow and level of expected profits of each VC in thefollowing way.

16

Proposition 6 When B is low in the sense that condition (3) holds, the deal flow of the two VCsis large, and only the most experienced VC earns positive expected profits. As B increases in thesense that condition (3) does not hold any more, the level of expected profits of the less experiencedVC increases, while that of the more experienced VC decreases. Also, the more experienced VCdeal flow decreases.

Clearly, the two VCs are not indifferent to the entrepreneur’s strategy choice. The moreexperienced VC strictly prefers the upfront competition, because it ensures him a high dealflow. Since he has an informational advantage over both the entrepreneur and the other VC,he is able to extract surplus from his superior signal. When negotiation is chosen, the moreexperienced VC receives only the deals that have been rejected by his competitor, which lowershis deal flow and his expected profit. At the opposite, the less experienced VC strictly prefers thenegotiation strategy since he can offer a deal without the fear of being challenged by a competitor.Proposition 6 also suggests that different types of VCs attract different types of entrepreneurs.If one assumes that different types of entrepreneurs exist in the economy, low-private benefitentrepreneurs send their projects to both inexperienced and experienced VCs, while high-privatebenefit entrepreneurs favor less experienced VCs. Overall, the deal flow of less experienced VCsis higher than that of more experienced venture capital firms.

The next proposition concludes on the efficiency of the entrepreneur’s decision.

Proposition 7 There is less overinvestment when the entrepreneur initiates upfront competition(i.e. when condition (3) holds), than when the entrepreneur negotiates with the less experiencedVC.

The result stated in proposition 7 follows from the previous discussions on the level of over-investment induced by the two fund-raising strategies. The efficient investment decision is tofinance projects if and only if the more experienced VC has received a high signal. In all the othercases, the investment project has, by assumption, a negative social NPV. Under negotiation, theprobability to finance a project is:

probHα + probHα,Lα ,

which is equal toprobHα + probHα,Lα .

Under competition, the probability to finance a project is:

probHα + probHα,Lαx.

In both cases, there is overinvestment, since all positive NPV, but some negative NPV projectsare financed. However, there is less overinvestment in the upfront competition strategy.

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6 Empirical predictions

The entrepreneur’s optimal fund raising strategy obviously influences the performance of theventure capital industry, and the returns earned by the two VCs. The empirical implications ofour results are two-fold. First, our results state that depending on the level of private benefits, theventure capital industry falls into one of two competition regimes, and the overall performanceof venture capital investments differs. More precisely, we expect the performance of the venturecapital industry to be larger when the entrepreneur’s private benefit of control is low. This isbecause when private benefits are low, entrepreneurs optimally choose to set fierce competition,and less experienced VCs refrain from offering deals. Since their screening process is not as goodas that of experienced VCs, their refraining from investing is good news: less bad projects areselected, and total industry performance (measured by the quality of the projects undertaken)increases, as stated in proposition 7. To assess the relevance of this result, the empirical challengeis to measure the level of private benefits of entrepreneurs. One possibility is to consider thatprivate benefits measure the future ability of entrepreneurs to divert firms’ resources. The qualityof the corporate governance can be an (inverse) measure of future private benefits. In that case,the model predicts that when corporate governance is good, the selection rate is lower (i.e. thefraction of investment proposals that are financed), and the venture capital industry performanceincreases. This can explain observed performance gap across countries (see e.g. Hege et al.(2006)), or the fact that VCs investment choices vary with the legal context.

Second, in each competition regime, our results predict that the relative financial performanceof more and less experienced funds varies, because their financial offers, and selection strategyvary. Proposition 6 states that the expected profits of experienced (resp. less experienced) VCsdecrease (resp. increase) when private benefits increase. It is not easy though to observe theperformance of a single fund over different market environments, usually because venture capitalfunds operate in specialized markets and geographic areas. To provide testable predictions ofthese results, we need to assess the relative performance of each fund, in each competitionregime. Also, empirical evidence on the performance of venture capital funds usually measuresthe profitability of the realized investments, while our results are based on unconditional expectedprofits. To obtain testable predictions, we need to compute the VCs expected profits, conditionalon financing taking place. The next proposition summarizes these findings.

Proposition 8 When the entrepreneur sets upfront competition (condition (3) holds), the moreexperienced VC earns higher profits on investment than the less experienced VC. When the en-trepreneur initiates negotiation, the more experienced VC’s profits on investment can be higheror lower than those of the less experienced VC.

The intuition of the proposition is the following. Under upfront competition, only the more

18

experienced VC earns positive expected profits. These profits are nothing but the expectedprofits on investment multiplied by the probability to invest in a deal. As a consequence, the(expected) profits on investment are nul for the less experienced VC, and positive for the moreexperienced VC. Things are more complicated in the negotiation regime, because the two VCsearn positive expected profits. The relative profitability of the two VCs depends on two elements.First, the less experienced VC has the advantage to play first, and to finance all projects for whichhe receives a high signal, which raises the profitability of his investments. But the second VChas a better screening ability, which may increase his profitability. Our model thus predicts thatmore experienced VCs perform better when competition is intense, and private benefits are low,while this needs not be the case when competition is less severe (i.e. when private benefits arelarge, or when corporate governance is weak). These results speak to the empirical findings ofKaplan and Schoar (2005), and Hege et al. (2006). While the former document some persistencein VC funds performance in the US, suggesting that more experienced or skilled VCs are able togenerate larger returns, Hege et al. (2006) find that US VCs do not outperform European VCswhen investing in European deals. Our model can reconcile the two by showing that experiencealone cannot explain profitability: one needs to consider also the nature of competition.

7 Extension: syndication decision

So far we assumed that venture capitalists cannot communicate to propose a single joint offer.This however can be done in practice through a syndicated offer. The current setting allows todiscuss the incentives of the two VCs to make a joint offer rather than two competing offers.Assume that the two VCs can, instead of making competing bids, share their information andmake a joint offer. For simplicity, suppose that they have the same bargaining power, so thatthey split evenly the surplus from the joint offer. The basic idea is that venture capitalistswhen deciding to syndicate, compare their standalone expected profit to their share of the jointmonopoly profit.18 Suppose first that the entrepreneur triggers upfront competition. In thatcase, we know from proposition 1 that V Cα’s expected profit is zero: he is therefore alwaysinclined to syndicate with V Cα to increase his profit. This is not necessarily true for V Cα

though. Two reasons explain his reluctance to syndicate. First, he is able to capture positiveprofits in the competition game. Second, since his competitor’s signal has no value (i.e. does notaffect his investment decision), he cannot increase total monopoly profits through syndication. Ofcourse, his standalone profits are reduced by competition, which implies that he sometimes findsit profitable to collude with his competitor. Intuitively, he does so if he is not too experiencedcompared to his competitor. In addition, it is likely that syndication is less frequent in the

18See Casamatta and Haritchabalet (2007) for a complete analysis of this trade-off. See also Biais and Perotti(2003) and Cestone, Lerner, and White (2006) on the issue of private signals revelation through joint investment.

19

negotiation game. First, the above argument still goes through. Second, V Cα is less likely toaccept syndication because he manages to earn monopoly profits at the initial negotiation stage.Therefore, for syndication to occur, it must also be the case that the second signal increasessubstantially the total value of the investment project.

This is formally stated in the next proposition.

Proposition 9 In the upfront competition game, the two VCs syndicate if and only if the fol-lowing condition holds:

q(Hα)(q(Hα)pR− I

)− 1

2q(Hα) (q(Hα)pR− I) ≥ 0. (4)

In the negotiation game, the two VCs syndicate if condition (4) holds and if the followingcondition is satisfied:

12probHα/Hα

(q(Hα, Hα)pR− I) ≥ q(Hα)pR− I. (5)

Suppose that α is fixed, and let α vary. The left-hand side of condition (4) increases withα. One sees easily that the left-hand side of condition (4) is negative when α tends to αmin: inthat case, syndication does not take place. At the opposite, when α tends to α, the equation isalways satisfied. We can conclude that syndication is more likely to appear when there is nottoo much heterogeneity in the industry.

8 Conclusion

In this paper, we investigate how competition takes place in the VC industry for entrepreneurswho seek financing for innovative projects. We consider a model whereby a cash-poor en-trepreneur proposes an investment project to venture capitalists. We compare the utility thatthe entrepreneur can obtain when he proposes his project to two VCs at the same time and whenhe starts negotiating with one VC only, postponing competition. Some important assumptionsdrive the results of the model. First, venture capitalists are able to extract private informationon the true value of the project, which constitutes an informational advantage when dealing withthe entrepreneur. Second, VC financing is in excess supply, and the entrepreneur faces severalinvestors to send his project to. Next, to feature in a realistic way the heterogeneity in theVC industry, we assume that VCs have different signal precisions, which make them more orless vulnerable when competing with each other. As a consequence, their equilibrium strategiesand expected profits are different. Last, the entrepreneur enjoys non monetary benefits whenhis project is implemented. When deciding his optimal fund-raising strategy, he cares not only

20

about his expected monetary profits, but also about his expected private benefits. This affectsthe efficiency of the investment decision, and the performance of the industry.

Our results are that, first, the entrepreneur cannot use the threat of competition to extractprofit when negotiating with one VC only. Either he accepts any offer by the first VC, andmakes zero profits, or he always enforces competition. This last equilibrium does not alwaysexist because enforcing competition is costly for both the entrepreneur and the initial venturecapitalist. Winner’s curse at the competition stage makes the entrepreneur more willing to findan agreement at the initial stage of negotiation, which destroys his bargaining power. Second, theoptimal fund-raising strategy of the entrepreneur depends on his level of private benefit. Whenhis private benefit is low, he favors upfront competition, which leads to a high deal flow for bothVCs, positive expected profits for the more experienced VC, and zero expected profits for theless experienced VC. It means that the less experienced VC cannot earn more than the relevantmarket return given the project risk. When the level of private benefit is high, the entrepreneurprefers to start negotiating with the less experienced VC first. This raises the latter’s expectedprofit, and reduces both the deal flow and the expected profit of the more experienced VC.Finally, this strategy reduces efficiency in the sense that more negative-social NPV projects arefinanced.

21

Appendix

Proof of proposition 1

Suppose first that V Ci anticipates that γ∗j (L) = ∅. Then announcing γi(L) = ∅ is clearly a dominantstrategy, since the maximum profit that V Ci can obtain is : NPV (q(Li)) < 0.

Suppose next that V Ci anticipates that γ∗j (L) = γ∗j > 0, and that γ∗j (H) = γ∗∗j > 0. For V Ci tomake a bid after a low signal, he must win more often when V Cj has received a high signal than whenV Cj has received a low signal. This anticipation on V Cj ’s strategies is clearly not rational since thelatter would make negative profits.

We thus obtain that V Cj does not make any offer when sj = L. Let us establish that there is nopure strategy equilibrium when si = H. Suppose that V Ci anticipates that γ∗j (H) = γ∗j . The expectedpayoff of V Ci is:

probLj/Hi(γiq(Hi, Lj)pR− I) if γi > γ∗j ,

probLj/Hi(γiq(Hi, Lj)pR− I) + probHj/Hi

λ(γiq(Hi,Hj)pR− I) if γi = γ∗j ,

probLj/Hi(γiq(Hi, Lj)pR− I) + probHj/Hi

(γiq(Hi,Hj)pR− I) if γi < γ∗j ,

where probLj/Hidenotes the probability that V Cj receives a low signal given that V Ci has received a

high signal. When both VCs make the same bid, we assume that the probability that V Ci wins is equalto λ.

See first that if γi = γ∗j , one can always find ε > 0 such that if V Ci prefers not to deviate (i.e. if λ

is high enough), this is not an equilibrium strategy for V Cj , who prefers to deviate and undercut V Ci’sbid.

Define γ̂i as follows:

max[0, probLj/Hi(q(Hi, Lj)pR− I)] = probLj/Hi

(γ̂iq(Hi, Lj)pR− I) + probHj/Hi(γ̂iq(Hi,Hj)pR− I).

γ̂i is the bid such that V Ci is indifferent between bidding γ̂i if he wins with probability one, and biddingthe highest possible bid, if he wins only when V Cj has received a low signal. Note that the less experiencedVC bids nothing if he wins only when the other signal is low, while the most experienced VC bids 1 inthat case. Therefore:

γ̂α =I

q(Hα)pR,

γ̂α =probLα/Hα

(q(Hα, Lα)pR− I) + I

q(Hα)pR.

We have that γ̂α < γ̂α if

I

(q(Hα)q(Hα)

− 1)

> probLα/Hα(q(Hα, Lα)pR− I).

Note thatq(Hα)q(Hα)

=αq0[αq0 + (1− α)(1− q0)]αq0[αq0 + (1− α)(1− q0)]

22

and

probLα/Hα(q(Hα, Lα)pR− I) =

α(1− α)q0

αq0 + (1− α)(1− q0)pR− I

α(1− αq0) + α(1− α)(1− q0)αq0 + (1− α)(1− q0)

.

Therefore γ̂α < γ̂α is equivalent to

α[(I − q0pR)(1− α)(α− I(1− q0)q0pR− I

)] > I(1− q0)α(1− α).

Observe that the LHS is always positive when q0pR− I is negative so that this condition boils downto

α >I(1− q0)α

α(I − q0pR) + I(1− q0),

which is always satisfied when q(Hα, Lα)pR− I > 0.

If γ∗α < γ̂α, then the optimal strategy of V Cα is to play γα = ∅. In this case, the optimal strategyof V Cα is to play 1, hence this is not an equilibrium. If γ∗α > γ̂α, then V Cα optimally plays γ∗α − ε, butV Cα wants to deviate from his initial strategy. Hence this is not an equilibrium. Finally, if γ∗α = γ̂α,V Cα makes negative profits and prefers to play ∅. In that case, V Cα increases his bid. Therefore, thereis no pure strategy equilibrium when a VC observes a high signal.

The above analysis states that there is no pure-strategy equilibrium in the upfront competition game.We first look for the bounds of the support of the mixed-strategy equilibrium. Recall that γ̂α > γ̂α. V Cα

and V Cα thus play a mixed strategy with support [γ̂α, 1].

Clearly, for V Cα to play a mixed strategy with support Σα = [γ̂α, 1], it must be the case that V Cα

plays 1 with strictly positive probability (otherwise, V Cα makes negative profits when bidding 1). This isonly possible if V Cα does not participate with strictly positive probability (otherwise, the expected profitof V Cα is lower when he bids 1 than when he bids γ̂α). Therefore, the equilibrium we are consideringhas the following features: after receiving a high signal, V Cα, with probability x, randomizes accordingto the continuous distribution F (γ) on [γ̂α, 1] and, with probability (1− x), bids 1. After a high signal,V Cα, with probability x, randomizes according to the continuous distribution F (γ) on [γ̂α, 1] and, withprobability (1− x), does not participate.

To determine the distribution function of the mixed strategy, recall that by definition, for eachstrategy γα played by V Cα, his expected profit must be equal to : I

(q(Hα)q(Hα) − 1

). In particular, when

V Cα bids 1, at equilibrium we must have:

probLα/Hα(q(Hα, Lα)pR− I) + probHα/Hα

(1− x)(q(Hα,Hα)pR− I) = I

(q(Hα)q(Hα)

− 1)

.

This is equivalent to :

x =(1− I

q(Hα)pR )(q(Hα)pR)

probHα/Hα(q(Hα,Hα)pR− I)

.

See that x is strictly positive since 1− Iq(Hα)pR > 0.

23

By the same reasoning, for any γα in [γ̂α, 1], we must have:

F (γ) =(γ − I

q(Hα)pR )q(Hα)pR

xprobHα/Hα(γq(Hα,Hα)pR− I)

.

It is easy to see that F has all the properties of a distribution function : F is increasing in γ,F (γ̂α) = 0, and F (1) = 1.

Similarly, for each strategy γα played by V Cα, his expected profit must be equal to zero. In particular,if γ = 1, we must have:

probLα/Hα(q(Hα, Lα)pR− I) + probHα/Hα

(1− x)λ(q(Hα,Hα)pR− I) = 0.

This is equivalent to:

1− x =probLα/Hα

(I − q(Hα, Lα)pR)probHα/Hα

λ(q(Hα,Hα)pR− I).

See that 1− x is strictly positive, and strictly lower than 1 if λ is large enough (in particular, this isalways true for λ = 1).

As before, imposing that V Cα’s expected profit is equal to zero for any bid γ defines the probabilitydistribution function F .

�

Proof of proposition 2

Consider an equilibrium candidate in which V C1, whatever his level of experience, plays γ1 = ∅ ifs1 = L, and γ1 = 1 if s1 = H. Suppose next that V C2 believes that any offer by V C1 is acceptedby the entrepreneur. His equilibrium belief is thus that s1 = L if he is contacted. Given his belief, heplays γ2 = ∅ if s2 = L, and γ2 = ∅ if he is less experienced, or γ2 = 1 if he is more experienced, ifs2 = H. Given V C2’s equilibrium strategy, the entrepreneur accepts V C1’s offer, because he cannot earnmore by enforcing competition. If he does, V C1 plays 1 (if he is more experienced) or 1 − ε (if he isless experienced). The entrepreneur’s expected utility if thus q(H1)B if he accepts the initial offer. If heenforces competition, his expected utility is q(H1)B−ξ if V C1 is experienced and q(H1)B−ξ+ε(q(H1)pR)if he is less experienced. When ε is sufficiently low, the entrepreneur optimally accepts the first-stageoffer.

�

Proof of proposition 3

1) Suppose that the entrepreneur contacts V Cα first. We show that there is no equilibrium in whichthe entrepreneur rejects V Cα’s offer with probability δ > 0. Consider such an equilibrium candidate, in

24

which V C1 makes an offer γ1 when s1 = H, and no offer when s1 = L, and in which the entrepreneurreject V C ′

1s offer with probability δ > 0 so that V C2 wants to participate if he receives a high signal.

Suppose that δ < 1. In that case, the entrepreneur plays a mixed strategy. The minimum feasible bidof V C2 (γ̂2(δ)) verifies that V C2 is indifferent between bidding γ̂2(δ) and winning with probability one,and bidding nothing. We thus have γ̂2(δ) = I

q(H2,δ)pR , where q(H2, δ) represents the probability that thequality of the project is good given that V C2 has received a high signal and that he believes that anyoffer of V C1 is rejected with probability δ. We have:

q(H2, δ) =q0α2(α1δ + (1− α1))

q0α2(α1δ + (1− α1)) + (1− q0)(1− α2)(α1 + (1− α1)δ).

One can show that q(H2, δ) increases with δ so that γ̂2(δ) decreases with δ. Therefore, if the gamereaches the competition stage, the equilibrium strategies are those defined in proposition 1. The expectedutility of the entrepreneur, if he rejects V C1’s offer, and enforces competition is written:

E(UE(δ < 1)) = probH2/H1 [x2(δ){Eγ1<γ2q(H1,H2, δ)(pR(1− γ1) + B)

+Eγ1>γ2q(H1,H2, δ)(pR(1− γ2) + B)}

+(1− x2(δ))EF1q(H1,H2, δ)(pR(1− γ1) + B)]

+probL2/H1 [EF1q(H1, L2, δ)(pR(1− γ1 + B))]− ξ,

(6)

where Eγ1<γ2 denotes the expectation operator given that γ1 < γ2, and EF1 denotes the expectationoperator over the whole distribution function F1. Note that since the entrepreneur knows that s1 = H,and since V C1 is more experienced, he expects to be financed with probability one at the competitionstage. After manipulations, equation (6) leads to:

E(UE(δ < 1)) = q(H1)(pR + B)− ξ − I − (γ̂2(δ)q(H1)pR− I)

−probH2/H1x2(δ)Eγ1>γ2(q(H1,H2, δ)γ̂2(δ)(pR− I).

The entrepreneur’s expected utility is equal to his expected private benefit B, plus the project’s NPVgiven V C1’s signal, minus the expected profit of V C1 under competition, (this profit is positive sinceγ̂2(δ) > γ̂1, minus a third positive term. This third term represents the (positive) expected profit thatmust be left to V C2 when s1 = H to compensate his loss when V C2 bids and s1 = L.

The surplus that the entrepreneur and V C1 can share under negotiation is equal to q(H1)(pR+B)−I.Therefore, E(UE(δ < 1))+E(ΠV C1) < q(H1)(pR+B)−I, where E(ΠV C1) is V C1’s expected profit undercompetition. This implies that V C1 can always propose γ1 such that he and the entrepreneur are bothbetter off negotiating than going to the competition stage. In other words, for any δ < 1, V C1 alwayswants to deviate from the offer that makes the entrepreneur indifferent between accepting and rejectingthe offer : V C1 makes a strictly better offer to the entrepreneur who always accepts. As a consequence,the equilibrium candidate in which δ < 1 does not exist.

Suppose next that δ = 1. By analogy with the above case, when the entrepreneur always enforcescompetition, his expected utility is equal to:

E(UE) = q(H1)(pR + B)− ξ − I − (γ̂2q(H1)pR− I)

−probH2/H1x2Eγ1>γ2(q(H1,H2)γ2pR− I).

25

The entrepreneur’s expected utility is just the project’s NPV given V C1’s signal, minus the positiveexpected profit of V C1 under competition, minus the positive rent left to V C2 when s1 = H, plus theexpected private benefit. The surplus that the entrepreneur and V C1 can share under negotiation isequal to q(H1)(pR + B) − I. Therefore, V C1 can always propose γ1 such that he and the entrepreneurare both better off negotiating than going to the competition stage, and the above equilibrium candidatedoes not exist. In equilibrium, when the entrepreneur contacts the more experienced VC first, δ = 0 andthe entrepreneur obtains zero profit.

2) Suppose next that the entrepreneur contacts V Cα first. Consider an equilibrium candidate inwhich V C1 makes an offer γ1 when s1 = H, and no offer when s1 = L. Again, assume δ > 0, so that V C2

participates if he is contacted and receives a high signal. We have γ̂1 > γ̂2(δ = 1). However since γ̂2(δ)is decreasing with δ, the minimum bid of V C2 can be larger or smaller than the minimum bid of V C1.

Consider first the values of δ such that γ̂1 > γ̂2(δ). The equilibrium strategies are those defined inthe first part of the proof and we know that an equilibrium in which 0 < δ < 1 does not exist.

If δ = 1, the expected utility of the entrepreneur, if he always refuses the offer of V C1 and enforcescompetition (δ = 1) is written:

E(UE) = probH2/H1 [x1 {Eγ1<γ2q(H1,H2)((1− γ1)pR + B) + Eγ1>γ2q(H1,H2)(pR(1− γ2) + B)}

+(1− x1)EF2q(H1,H2)(pR(1− γ2) + B)] + probL2/H1x1[EF1q(H1, L2)(pR(1− γ1) + B)]

−[probH2/H1 + probL2/H1x1]ξ.

After manipulations, the entrepreneur’s expected utility if he enforces competition becomes:

E(UE) = x1(q(H1)pR− I) + probH2/H1(1− x1)(q(H1,H2)pR− I)

−probH2/H1 [(1− x1)EF2(γ2q(H1,H2)pR− I)− x1Eγ1>γ2(γ2q(H1,H2)pR− I)]

+[probH2/H1q(H1,H2) + probL2/H1q(H1, L2)x1]B − [probH2/H1 + probL2/H1x1]ξ.

Recall that the profit of V C1 at the competition stage is zero in expectation. Therefore the jointprofit of the entrepreneur and V C1 at the competition stage is larger than the surplus they share undernegotiation iff:

E(UE) > q(H1)(pR + B)− I.

Formally, there exists an equilibrium in which the entrepreneur always refuses V C1’s offer, and enforcescompetition iff:

probH2/H1 [(1− x1)EF2(γ2q(H1,H2)pR− I)− x1Eγ1>γ2(γ2q(H1,H2)pR− I)] (7)

< (1− x1)probL2/H1(I − q(H1, L2)(pR + B))− ξ[probH2/H1 + probL2/H1x1].

When equation (7) holds, the joint profit of the entrepreneur and V C1 increases if competition is enforced,compared to the negotiation stage. This equilibrium can occur because the second signal increases thevalue of the project. This can overcome the rent left to V C2 when s1 = H. The LHS of equation (7)represents the rent to be left to V C2 when s1 = H, and the RHS represents the increase in the project’sNPV after the second signal. Competition is valuable because V C1 does not always bid when s2 = L,therefore some negative NPV projects are not financed (while they would be at the negotiation stage).

26

Note that the benefit of competition is mitigated by the loss of the expected private benefit B when suchprojects are not financed anymore. Intuitively, when B is large, the benefit of competition vanishes. Ifthe former effect is smaller than the latter, V C1 cannot make an offer that discourages competition, andan equilibrium in which the entrepreneur always enforces competition (i.e. δ = 1) exists.

Consider next the values of δ such that γ̂1 < γ̂2(δ). When V C2 believes that V C1’s offer is rejectedwith probability δ, his minimum bid is defined as follows :

γ̂2(δ) =probL1/H2,δ(q(H2, L1, δ)pR− I) + I

q(H2, δ)pR. (8)

Equation (8) is equivalent to:

γ̂2(δ) =q0α2(1− α1)pR + δI[q0α1α2 + (1− α1)(1− α2)(1− q0)]

α2q0(α1δ + (1− α1))pR. (9)

Using equation (9), condition γ̂1 < γ̂2(δ) holds if and only if :

δ <α2[q0α1pR− I(α1q0 + (1− α1)(1− q0))]

Iα1(1− q0)(2α2 − 1)(10)

It is easy to see that this condition can be satisfied since the RHS is positive. In that case, V C2 doesnot want to bid until γ̂1 since he can obtain a strictly higher expected payoff by bidding 1 each time hereceives a high signal. Therefore, he randomizes over a strictly smaller interval: he bids less aggressively.This implies that V C1 never bids below γ̂2(δ), and that he also earns positive expected profits.

We now characterize the mixed strategy equilibrium when the minimum bid of each VC is γ̂2(δ).When V C2 receives a high signal, with probability x2(δ), he randomizes according to the continuousdistribution F2(γ) on [γ̂2(δ), 1] and, with probability (1 − x2(δ)), he plays γ∗2 = 1. When V C1 receivesa high signal, he randomizes according to the continuous distribution F1(γ) on [γ̂2(δ), 1]. The expectedprofit of V C2 is strictly positive and equal to probL1/H2,δ(q(H2, L1, δ)pR − I). The expected profit ofV C1 is also positive and equal to γ̂2(δ)(q(H1)pR− I).

Proceed as in proposition 1 to determine that in equilibrium, V C2, after a high signal, plays 1 withprobability 1 − x2(δ) and with probability x2(δ) randomizes according to the continuous distributionF2(γ) on [γ̂2(δ), 1] where

1− x2(δ) =γ̂2(δ)

q(H1)pR− I + probL2/H1(I − q(H1, L2(δ))pR)probH2/H1(q(H1,H2(δ))pR− I),

andF2(γ) =

(γ − γ̂2(δ))q(H1)pR

probH2/H1x2(δ)(γq(H1,H2, (δ))pR− I).

After a high signal, V C1 randomizes according to the continuous distribution F1(γ) on [γ̂2(δ), 1] where

F1(γ) =γq(H2, δ)pR− I − probL1/H2,δ(q(H2, L1, δ)pR− I)

probH1/H2,δ(γq(H1,H2, δ)pR− I).

The expected utility of the entrepreneur, if he refuses the offer of V C1, given that V C2 believes thatany offer of V C1 is rejected with probability δ such that γ̂1 < γ̂2(δ), is written:

E(UE(γ̂1 < γ̂2(δ))) = probH2/H1 {Eγ1<γ2(1− γ1)q(H1,H2, δ)pR + Eγ1>γ2(1− γ2)q(H1,H2, δ)pR}+

probL2/H1 [EF1(1− γ1)q(H1, L2, δ)pR] + q(H1)B − ξ. (11)

27

Equation (11) can be simplified as follows:

E(UE(γ̂1 < γ̂2(δ))) = q(H1)(pR + B)− ξ − I − (γ̂2(δ)q(H1)pR− I)

−probH2/H1Eγ1>γ2(γ2q(H1,H2, δ)pR− I).

The entrepreneur’s expected utility is equal to the project’s NPV given V C1’s signal, minus the expectedprofit of V C1 under competition, minus the rent left to V C2 when s1 = H, plus the expected privatebenefit B. Clearly, E(UE(γ̂1 < γ̂2(δ)) + E(ΠV C1) < q(H1)(pR + B)− I. Therefore, V C1 can propose γ1

such that both he and the entrepreneur are better off negotiating than enforcing competition, and theabove equilibrium candidate does not exist.

�

Proof of proposition 5

When upfront competition is enforced, the expected utility of the entrepreneur is equal to the totalexpected monetary profits, minus the expected profit of V Cα, plus the expected private benefit. Formally,under upfront competition, we have:

E(UE) = probHα[q(Hα)(pR + B)− I] + probHα,Lα

x[q(Lα,Hα)(pR + B)− I]

−probHαI

[q(Hα)q(Hα)

− 1]

. (12)

When the entrepreneur initiates negotiation with the less experienced VC, he obtains:

E(UE) = probHαq(Hα)B + probLα,Hαq(Lα,Hα)B − probLα,Hαξ. (13)

Using equations (12) and (13), it follows that the entrepreneur prefers upfront competition iff:

B ≤probHα

(q(Hα)pR− q(Hα)

q(Hα)I)

+ probLα,Hαq(Lα,Hα)x(q(Lα,Hα)pR− I) + probLα,Hα

ξ

(1− x)probLα,Hαq(Lα,Hα)

.

�

Proof of proposition 6

Recall that the expected profit of V Cα is strictly positive and equal to probHα(q(Hα)pR− I) when the

entrepreneur starts negotiating. It is zero in the upfront competition game.

The expected profit of V Cα is probLα,Hα

(q(Hα, Lα)pR− I

)when the entrepreneur starts negotiating.

It is equal to probHα

(I( q(Hα)

q(Hα) − 1))

in the upfront competition game.

We know from proposition 1 that

probHα

(I

(q(Hα)q(Hα)

− 1))

> probHαprobLα/Hα

(q(Hα, Lα)pR− I

).

28

Given that probHαprobLα/Hα= probLα,Hα , we obtain that expected profits of V Cα are higher in the

upfront competition game.

�

Proof of proposition 8

For a given offer, the expected profit on investment (EΠ(V C/I)) is given by EΠ(V C/I) = EΠ(V C)pV C(I) , where

pV C(I) is the probability that V C’s offer is accepted, and where EΠ(V C) is the expected profit on eachoffer. Note that total expected profits are simply obtained by multiplying EΠ(V C) by the probability tomake an offer.

In the upfront competition game, for any offer, pV Cα(I) and pV Cα(I) are strictly positive. Moreover,the expected profit on each offer is constant (since VCs play in mixed strategies), and EΠ(V Cα) > 0 andEΠ(V Cα) = 0. As a consequence, we have :

EΠ(V Cα/I) > EΠ(V Cα/I) = 0

.

When the entrepreneur initiates negotiation, each offer is accepted with probability one (pV Cα(I) =

pV Cα(I) = 1) and each VC offers 1. Profits on investment are then given by Π(V Cα) = q(Hα)pR− I andΠ(V Cα) = q(Hα,Lα)pR− I.

Π(V Cα)−Π(V Cα) = [q(Hα,Lα)pR− I]− [q(Hα)pR− I] (14)

Equation (14) reduces to

Π(V Cα)−Π(V Cα) =α

(1− α)− α2

(1− α)2(15)

Equation (15) may be positive or negative, depending on parameter values.

Observe next that ∂(Π(V Cα)−Π(V Cα))

∂α > 0 and that ∃ ε = (2α−1)α(1−α)(1−α)2+α2 > 0 such that Π(V Cα) >

Π(V Cα) when α− α > ε.

�

Proof of proposition 9

Consider first the upfront competition game. Given that V Cα’s expected profit is zero in the upfrontcompetition game, V Cα always accepts to syndicate.

29

Next, we know from proposition 1 that in the upfront competition game,

EΠ(V Cα) = I

(q(Hα)q(Hα)

− 1)

Because the joint surplus is shared evenly in case syndication takes place,19 V Cα’s expected profitfrom syndication is given by: 1

2 (q(Hα)pR− I) .

V Cα chooses to syndicate iff:

12

(q(Hα)pR− I) ≥ I

(q(Hα)q(Hα)

− 1)

.

This equivalent to:

12

(q(Hα)pR− I) ≥ probLα/Hα(q(Hα, Lα)pR− I) + probHα/Hα

(1− x)(q(Hα,Hα)pR− I)

with

x =(1− I

q(Hα)pR )(q(Hα)pR)

probHα/Hα(q(Hα,Hα)pR− I)

.

After manipulations, this condition reduces to

q(Hα)(q(Hα)pR− I

)− 1

2q(Hα) (q(Hα)pR− I) ≥ 0. (16)

Consider now the negotiation game. We know from proposition 4 that the entrepreneur first contactsV Cα. In that case, V Cα’s expected profit is the same as in the upfront competition game. Condition 16is therefore necessary for V Cα to syndicate. In addition, V Cα accepts to syndicate only if his expectedprofit under syndication is larger than his expected profit under negotiation:

12probHα/Hα

(q(Hα,Hα)pR− I) ≥ q(Hα)pR− I.

�

19See Casamatta and Haritchabalet (2007)

30

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