DEALING WITH VENTURE CAPITALISTS: SHOPPING AROUND OR EXCLUSIVE NEGOTIATION

We study the optimal negotiation strategy of an entrepreneur who faces two investors with private information about his project’s proﬁtability. The entrepreneur derives a private beneﬁt of control so that he cares not only about expected monetary proﬁts, but also about the probability to obtain ﬁnancing. If he contacts both venture capitalists simultaneously, the entrepreneur obtains high expected monetary proﬁts. If he commits to a period of exclusive negotiation with one venture capitalist, he can increase the probability to obtain ﬁnancing for riskier projects


Introduction
Exclusive negotiations are frequent in financial transactions: Boone and Mulherin (2007) estimate that half of major takeover transactions between 1989 and 1999 occurred through private negotiations with a single bidder.They are also prevalent in early stage financing.For instance, venture capitalists' term sheets sometimes include exclusive negotiation periods, whereby entrepreneurs commit not to initiate talks with other potential financial partners during a predetermined period.
Relatedly, Hsu (2004) reports that about two-third of early-stage firms receive only one offer (but he does not measure the number of investors an entrepreneur negotiates with).Although such practices are hard to quantify in venture capital, they are an important issue for entrepreneurs searching financing. 1Exclusive negotiation probably benefits financial partners who can temporarily be protected from competitive pressure.The objective of this paper is to understand how it can also benefit entrepreneurs and to investigate the consequences of entrepreneurs' negotiation strategy on equilibrium financial contracts, valuations, and matching between entrepreneurs and venture capitalists.
The question of whether a seller prefers competition over negotiation has already been discussed in the literature.In particular, Bulow and Klemperer (1996) establish that when sellers value monetary profits only, an auction with N bidders always dominates negotiation with (N-1) bidders.This is hard to reconcile with observed exclusive negotiations.Our premise is that entrepreneurs in search of funds are not interested in monetary profits only.They also derive a private benefit when successfully funding their projects.These private benefits can reflect entrepreneurs' satisfaction to see their idea implemented, or their future reputation gains if the venture succeeds.Success can then increase entrepreneurs' perceived talent, and give them access to better job opportunities.We incorporate this assumption in a model of competition among asymmetrically informed venture capitalists (hereafter VCs).More experienced VCs are able to generate more precise information on the value of the entrepreneur's venture.This affects the expected profits the entrepreneur can capture when several VCs compete to finance his project, as well as the probability to get funded.
Because they care also about expected private benefits, entrepreneurs might choose another fund raising strategy.Our analysis builds on this fundamental insight.
Specifically, we consider a venture capital industry composed of two VCs with different screening abilities.The entrepreneur can choose one of two negotiation strategies to raise funds.Either he decides to shop for deals, and approaches the two venture capitalists simultaneously.Investors then offer menus of financial contracts.After observing his rival's offer, each investor subsequently chooses which financial contract to maintain from his menu.The sequential nature of the shopping around strategy allows to sustain pure-strategy equilibria according to the level of risk of the entrepreneurial venture.Riskier projects are financed by the experienced VC, who acquires an equity-like claim.Less risky projects are financed either by the inexperienced or the experienced VC.The inexperienced VC then acquires a debt-like claim.In both equilibria, VCs who provide funding at equilibrium earn strictly positive expected profits.A nice feature of these equilibria is that they characterize different situations of financial intermediation.The first equilibrium fits well with early-stage financing and venture capital: projects are particularly risky, investors who finance those ventures have better screening abilities and acquire equity claims.The second equilibrium corresponds to more standard entrepreneurial financing, whereby all types of financial intermediaries can provide funding.Interestingly, less experienced investors prefer to finance those ventures with debt.
The alternative strategy is for the entrepreneur to start exclusive talks with one venture capitalist, delaying the possibility to contact another venture capitalist later.At the equilibrium, the entrepreneur accepts any offer at the exclusive negotiation stage.The reason is that when negotiation fails after a period of exclusivity, subsequent investors infer bad news about the project quality and do not compete effectively.The entrepreneur's expected utility then reduces to his expected private benefit.This result confirms the intuition that exclusive negotiation is detrimental to entrepreneurs if one considers monetary profits only.However, the probability to obtain funding is large which can be appealing for high private benefit entrepreneurs.
The optimal negotiation strategy then results from a trade-off between monetary profits and the probability to get funded.Exclusive negotiation arises with high risk, high private benefit entrepreneurs.In all other situations, entrepreneurs prefer to shop around, but the nature of financial contracts, and the type of VCs they match with depends on the nature of their projects.Experienced VCs finance all types of projects, and acquire equity for the riskier ones.Inexperienced VCs only finance less risky projects, and acquire debt.The contribution of the paper is therefore two-fold.Firstly, we endogenously relate the type of financial contract issued to the characteristics of financial intermediaries.An important question in the literature is what makes venture capital different from traditional financial intermediation.We show that when investors with different screening ability compete with each other, riskier projects are financed with equity, and by the more able investors.Secondly, our paper is the first to provide a theoretical framework to understand when entrepreneurs find it optimal to engage in exclusive negotiation or to implement competition.
This gives rise to a number of new empirical predictions on VCs portfolio and deal flow, as well as on entrepreneurs' financial deals.An implication of the model is that inexperienced VCs should have a higher deal flow, and attract more entrepreneurs with riskier projects and higher private benefits than experienced VCs.Also, VCs are more likely to finance projects with equity-like claims when projects are riskier and VCs are more experienced.Regarding entrepreneurs, we expect first-time entrepreneurs to receive less offers on average than serial entrepreneurs, holding project risk constant.In addition, single offers are more likely to come from less experienced VCs which is consistent with empirical evidence.Last, pre-money valuations should be lower when entrepreneurs engage in exclusive talks, and receive only one offer at a time.The interest of our analysis is to explain why entrepreneurs optimally choose to relinquish bargaining power to VCs.
The paper is organized as follows.Next section presents the related literature.Section 3 describes the model and derives the first-best level of investment.Section 4 studies the outcome of the "shopping around" game.Section 5 derives the equilibria of the "exclusive talks" game.Section 6 studies the optimal negotiation strategy of the entrepreneur, and explores the empirical implications of our model.Section 7 discusses the robustness of our results to some alternative assumptions.
Section 8 concludes and proofs are provided in the appendix.

Related literature
Our paper is directly linked to the literature on competition between financial intermediaries with asymmetric information.Our shopping around game builds on the sequential setting of Broecker (1990), and extends it to the case in which investors have different signal precisions, and can design optimal financial contracts.The sequential game allows to obtain pure-strategy equilibria while mixed-strategy equilibria typically prevail in simultaneous competition games with discrete signals. 2 A novelty of our analysis is to derive the optimality of debt or equity claims according to the level of risk of projects, and to match financial contracts with investors' characteristics.Other papers study situations of informed investors and focus on the optimal contract design between investors and entrepreneurs: Inderst and Mueller (2006) consider a monopolistic informed investor, and show that the optimal financial claim depends on the bargaining power of the entrepreneur.We complement their analysis by explicitly considering competition.Axelson (2007) and Garmaise (2007) consider informed competitive investors, but study the case in which the firm can set ex ante the type of contract issued (Axelson (2007)), or the valuation rule used by the entrepreneur (Garmaise (2007)).Our paper takes the view that in early-stage financing, investors decide which contracts to offer.In addition, a distinctive feature of our analysis is that we endogenize what type of investors' competition the entrepreneur prefers to implement.This question is particularly relevant when investors cannot spot easily new investment opportunities.
Our emphasis on the trade-off between exclusive negotiation and competition is also linked to the auction-negotiation trade-off of Bulow and Klemperer (1996).Our analysis shares their result that an auction maximizes the expected monetary revenue of the seller.But in our setting, the entrepreneur also enjoys a private benefit, and therefore sometimes favors exclusive negotiation.An interesting feature of our setting is that when competition is efficient, it is not necessarily preferred by the entrepreneur.This is because the more experienced venture capitalist is able to capture part of the profits.This induces the entrepreneur to prefer exclusive negotiation that increases the probability to obtain financing when private benefits are high.This in turn leads to inefficiently high investment.Hellmann (2007) studies the optimal negotiation process chosen by an entrepreneur to obtain resources, assuming that investors can only be contacted sequentially.We consider instead the trade-off between simultaneous and sequential contacts.
In our model, entrepreneurs can perfectly identify potential financial partners, and their matching with a given partner results from their endogenous choice.Sørensen (2007) and Hong et al (2012) propose alternative models of matching in which better firms are associated with more experienced VCs because both attributes are complement.In their models, entrepreneurial projects' quality is public information and they do not study the asymmetric information bargaining process between VCs and entrepreneurs.Relatedly, Inderst and Mueller (2004) consider a search model according to which the probability to contact a partner depends on a matching technology, and on the relative supply and demand for venture capital.One result of their analysis is that venture capitalists make higher profits when competition is not too intense.This is consistent with our result that profits are higher for a venture capitalist with superior information.
The current paper is also related to the literature on venture capital financing.A major difference is that we focus on venture capitalists' screening role, rather than on their monitoring and value-added activities. 3The fact that some venture capitalists are more experienced than others has also been largely documented.Papers have explored how the level of experience of venture capitalists changes their behavior.Bottazzi, Da Rin, andHellmann (2008, 2009) find that more experienced venture capitalists, and venture capitalists operating in "better" legal systems are more actively involved in their portfolio firms.Experience also affects the decision to syndicate (Lerner (1994), Hopp and Rieder (2011), Casamatta and Haritchabalet (2007), Cestone, Lerner, and White (2007)) or the decision to exit (Gompers (1996)).None of these studies aims at understanding how heterogeneity in experience affects the nature of competition in the industry or the type of financial contract offered by venture capitalists.
3 The model

Investment project and returns
We consider a standard corporate finance model.An entrepreneur is endowed with a one-period innovative project that entails high potential returns, together with a high level of uncertainty.To capture these features, we make the following assumptions.
Firstly, the project return is risky.The future cash flow R is R S in case of success, and R F < R S in case of failure, with (R F , R S ) ∈ R 2 + .Also, the probability of success depends on the quality of the project which can be good (G) or bad (B).Success occurs with probability p > 0 if the project is good, and with probability p = 0 if the project is bad. 4 Last, the project requires an initial outlay Secondly, there is some uncertainty regarding the true quality of the project.Initially, all agents share the same prior belief that the project is good, denoted q 0 .To fit the situation of early-stage financing, we consider that the project is unprofitable based on prior beliefs.Assuming risk-neutral agents, and normalizing the riskless interest rate to zero, this implies The left-hand side states that the project net present value conditional on prior beliefs (denoted N P V 0 ) is negative, and the right-hand side states that the net present value of the G-type project is positive.

The venture capital industry
The entrepreneur is cash-poor, and must raise I from investors.Because N P V 0 < 0, he cannot raise funds from traditional investors, and turns to venture capitalists.Thanks to their experience at financing early stage ventures, VCs are able to (imperfectly) infer the quality of new projects. 5e assume that VCs perform investment analyses and observe at no cost a signal related to the project's true quality. 6This signal can be either high (s = H) or low (s = L) and its precision depends on venture capitalists' expertise α: P r(s = H|G, α) = P r(s = L|B, α) = α, where α > 1 2 .After observing their signal, VCs update their belief on the project quality using Bayes' rule.We denote q(s α ), the posterior probability that the quality of the project is good given that a VC with experience α has observed a signal s, and N P V (s α ) the corresponding net present value, conditional on the signal s.
The industry is heterogeneous, with some experienced VCs of type α = e and some inexperienced VCs of type α = i < e ≤ 1.This assumption captures realistic features of the industry, where some well-known and reputable venture capital funds compete with newer, less established funds.
We assume that there are two VCs in the economy, one experienced (V C e ) and one inexperienced We specify now the evolution of the project NPV conditional on signals.Firstly, any VC is sufficiently experienced so that the project NPV becomes positive conditional on observing a high signal.Were this not true, VC screening would be useless.Therefore: Secondly, to focus on the most interesting case, we assume that when screening by two VCs generates two opposite signals, the experienced VC's signal determines the sign of the project NPV.Extending the above notations to two signals, this means: From the investors' point of view, it is therefore optimal to undertake the project if and only if the experienced VC has observed a high signal.Note that in our model, experience only affects venture capitalists' screening ability.It would be plausible to also assume that experience allows venture capitalists to be more actively involved in their portfolio, thereby increasing the value of these new ventures.We discuss in section 7 the consequences of this additional assumption.

Entrepreneur's utility
The entrepreneur is risk neutral.On top of monetary payments, he enjoys a private benefit B 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 of entrepreneurship.Blanchflower and Oswald (1992) document from survey data the existence of non pecuniary benefits in entrepreneurship.In a similar spirit, Hamilton (2000) and Moskowitz and Vissing-Jorgensen (2002) find low monetary returns on entrepreneurial investments, and interpret these results as evidence of the existence of private benefits.In our setting, the private benefit is only enjoyed in case of success.This can reflect a possible "stigma of failure" incurred by entrepreneurs who do not succeed (see Landier (2005)), or equivalently the reputation gains enjoyed by the entrepreneur if the firm goes on.7 Therefore the utility of the entrepreneur is written where R .E denotes the entrepreneur's return according to the state of nature.For plausibility, we assume that B is not too large, so that it is optimal to implement the project if and only if V C e observes a high signal: The next two sections detail the extensive form of each game, and analyze the outcome of each negotiation strategy.Throughout the paper, our equilibrium concept is perfect Bayesian equilibrium.

Shopping around
Under this strategy, the entrepreneur contacts simultaneously the two VCs, who can offer a menu of contracts to finance the entrepreneur.A financial contract offered by V C α , with α ∈ {i, e}, is denoted (1, γ α ) where 1 = 1 if I is invested and 0 otherwise, and We assume that if no investment takes place, the VC cannot have a claim on the final cash flow : any strictly positive payoff implies 1 = 1.
After receiving offers, the entrepreneur can shop for deals, and show offers to competitors.In turn, each VC has the right to withdraw any offered contract before the entrepreneur's final choice.
The assumption of removable offers captures standard industry procedures, whereby VCs propose term sheets that can be used by entrepreneurs to shop around.Such term sheets are typically non binding (i.e. they can be removed).More precisely, the game considered is the following: 1.The two VCs privately observe their signal and make non binding offers, represented by menus C α of contracts γ α .
2. The entrepreneur shows (or not) each VC's menu of offers to his competitor.
3. Each VC chooses which offer(s) to maintain.8 4. The entrepreneur chooses his preferred remaining offer.

Preferences and contracts
To solve this game, it is useful to define a VC's maximum bid contract when he observes a high signal, γα .It is a contract such that a VC's profit when financing the entrepreneur with probability one (after a high signal) is equal to his reservation payoff.V C i 's reservation payoff is simply zero Conditions (2) reflect the fact that the entrepreneur is cash-poor.Denote Γ i the set of all contracts γi .Because N P V (H i ) > 0, Γ i is not empty.
Proceed as before to determine the set of V C e 's maximum bid contracts.A difference is that V C e 's reservation payoff is not zero because the project has a positive value when V C e observes a high signal whatever V C i 's signal.His reservation payoff, denoted Π(V C e ), is therefore his profit when he bids (R F , R S ) and finances the project only when s i = L: with RS e ≤ R S and RF e ≤ R F .
Again, we denote Γ e the set of all contracts γe .
The following lemma defines each VC's preferred contract in his competitor's indifference set, when he observes a high signal. .
Lemma 1 states that, among all contracts in Γ i , V C e prefers the contract with the highest payoff in the success state.The reason is that V C e 's signal is more precise than that of V C i .When he observes a high signal, he is more optimistic than V C i (q(H e ) > q(H i )).He therefore prefers the contract γe i that "load" most on the success state.9Symmetrically, V C i is more pessimistic than V C e , and prefers the contract γi e with the highest payoff in the failure state.
Similarly, the entrepreneur's preferred contract depends on his belief.If he has no information about the distribution of states, he prefers the contract that pays him R F in case of failure, among contracts in Γ i (resp.Γ e ).This is because V C i (resp.V C e ) is more optimistic about the probability of success than the entrepreneur.If at the opposite, the entrepreneur is more optimistic than V C i (resp.V C e ), he prefers the contract in Γ i (resp.Γ e ) that maximizes his payoff in the success state.
This happens for instance if the entrepreneur believes that both VCs have observed a high signal.10 Condition ( 5) can be interpreted as follows.If the return that can be pledged to the venture capitalist in the failure state is too small, V C i suffers from having a less precise signal, and requires a higher return in the success state to maintain a constant (zero) profit.In that case, all contracts in Γ i offer V C e a profit strictly larger than his reservation payoff (i.e.any contract in Γ i is such that At the opposite, when R F is large, it is possible to offer contracts granting a large payoff in the failure state to the venture capitalists.These contracts are preferred by V C i , and provide V C e a profit strictly smaller than his reservation payoff.This second case is illustrated in Figure 1 by the fact that the Γ i curve is below the Γ e curve for contracts satisfying R F α ≥ R F .

Equilibrium
The following proposition presents pure strategy equilibria of the shopping around game.
Proposition 1 When condition (5) holds, there exists a pure-strategy equilibrium such that V C e ultimately maintains the contract γe i when he observes s e = H, and the null contract when he observes s e = L, and such that V C i ultimately maintains the null contract whatever his signal.
When condition (5) does not hold, there exists a pure-strategy equilibrium such that V C i ultimately maintains the contract γi e when he observes s e = H, and the null contract when he observes s e = L, and such that V C e ultimately maintains (R F , R S ) when s e = H and the null contract otherwise.
Two different financing regimes arise.When R F is small, the equilibrium is sustained by the following strategies.Whatever the signal observed, V C i offers the same menu of two contracts: the null contract, and the entrepreneur's preferred contract on Γ i when he infers two high signals.
But on the equilibrium path, V C i only maintains the null contract.V C e offers a menu of three contracts: the null contract, his preferred contract on Γ i (γ e i ), as well as the entrepreneur's preferred contract on Γ i .When s e = L, V C e only maintains the null contract.When s e = H, V C e only maintains γe i .The intuition for that result is the following.When R F is small, any contract acceptable for V C i yields strictly positive profits for V C e because of his information advantage.
V C i 's strategy is therefore to offer his best possible contract to prevent deviations from V C e .For this threat to be credible, V C i proposes the entrepreneur's preferred contract in Γ i , so that V C i 's offer is indeed chosen against any profitable offer by V C e .This contract is withdrawn at the equilibrium, which allows V C e to ultimately offer his preferred contract in Γ i .Symmetrically, to prevent deviations from V C i , V C e also offers the entrepreneur's preferred contract in Γ i : this second contract is withdrawn if V C e observes no deviation.
This highlights two interesting features of our equilibrium.Firstly, the presence of V C i forces V C e to offer a contract that leaves V C i indifferent between participating or not.This limits the profits that V C e can extract thanks to his informational advantage.Secondly, since when R F is small V C i never finances the entrepreneur at equilibrium, V C e is able to select his preferred contract among all contracts that make V C i indifferent.That V C e is able to offer γe i is not straightforward, because this contract a priori leaves room for deviations that are profitable both for V C i and for the entrepreneur.V C e is able to prevent these deviations by offering a menu of contracts (including his preferred contract and the entrepreneur's preferred contract in Γ i ) thereby forcing V C i to remove any investment offer.It is worthwhile mentioning that the equilibrium contract is different if V C e is restricted to offer only one contract (along with the null contract).This point, and the resulting equilibrium, are discussed at the end of the section.
The second financing regime corresponds to the case when R F is large.The above described equilibrium cannot be sustained anymore because when V C i offers the entrepreneur's preferred contract in Γ i , V C e is better off not offering a competitive bid.11V C i can exploit this situation to increase his expected profit, up to the point at which V C e is indifferent between participating or not.As a consequence, the equilibrium contract now lies in Γ e .At the equilibrium, V C e offers the entrepreneur's preferred contract in Γ e to prevent deviations from V C i .When observing no such deviations, V C e withdraws this offer, and maintains only the monopoly offer (R F , R S ).The entrepreneur is therefore financed by V C i when s i = H, and by V C e when s i = L and s e = H.
In our equilibria, VCs have different project valuations because they cannot infer their rival's signal before making their decision to maintain an offer.This allows to draw an analogy with Bertrand competition games with asymmetric costs.In these games, the typical equilibrium entails that the low cost firm serves the whole market at a price equal to its competitor's marginal cost.In our model, this translates into the fact that accepted contracts lie on the reservation profit line of the "high cost" venture capitalist. 12It is well known that other equilibria can arise in this setting, with equilibrium prices strictly lower than the highest marginal cost.This corresponds in our setting to one VC offering a contract that grants him less than his reservation payoff, were this contract chosen at equilibrium.The following corollary states that such equilibria cannot be sustained in our setting.
Corollary 1 Consider any pure strategy equilibrium such that VCs offer the same menu regardless of their signal.When condition (5) holds, any non null contract offered at equilibrium is on Γ i .
When condition (5) does not hold, any non null contract offered at equilibrium is on Γ e or is the monopoly contract.
Corollary 1 characterizes what contracts can be offered when initial offers do not convey information to competitors.See first that the entrepreneur cannot obtain a more favorable contract than those granting V C i (or V C e , when (5) does not hold) his reservation payoff.In our setting, a venture capitalist cannot offer a contract below his reservation profit line, because of the two stage structure.Consider the case in which (5) holds.For any such contract to be offered at equilibrium, V C i must be willing to maintain this contract (at the last stage) if he observes that V C e deviates.This is clearly not a best response (V C i makes negative expected profits with contracts below Γ i ), which allows V C e to deviate in the first place.Therefore the existence of a second decision stage eliminates the dominated strategies these equilibria typically rely upon.Next, because of competition, there cannot be an equilibrium in which the entrepreneur is ultimately financed with a contract that is strictly "above" Γ i .That is, V C e cannot earn a profit higher than that provided by γe i because V C i would deviate.

Debt or equity offers ?
In order to determine what financial contracts are offered at equilibrium, we need to discuss whether the equilibrium presented in Proposition 1 is unique. 13When condition (5) holds, it is possible to sustain equilibria in which any contract on Γ i is ultimately offered by V C e . 14However, such equilibria rely on the rather unappealing assumption that V C i has different responses to different contracts offered on his indifference curve.In particular, for a contract γ * = γe i to be offered at equilibrium by V C e , it has to be the case that V C i threatens to maintain γE i following any offer γ ∈ [γ e i , γ * ), and to remove it following any offer γ ∈ [γ * , γE i ].If we assume instead that V C i has the same response to all contracts offered on his indifference curve, only γe i can be ultimately offered to the entrepreneur.To be able to explore the properties of the equilibrium financial contracts, we maintain this assumption in the remainder of the paper.
Interestingly, the existence of two different financing regimes allows to relate the type of financial contracts traded at equilibrium to the intrinsic characteristics of the entrepreneur's project, as stated in the following corollary.
Corollary 2 When condition (5) holds, V C e acquires an equity-like claim.When condition (5) does not hold, V C i acquires a debt-like claim, and V C e 's claim is indeterminate.
The proof of corollary 2 is immediate.Recall that when (5) holds, V C e ultimately offers γe i = I−q(H i )pR S 1−q(H i )p , R S .This contract pays proportionally more in the success state than in the failure state.This implies that it cannot be replicated by a debt, or a convertible debt claim.Instead, it can be replicated by a mix of equity and stock options.For that reason, we loosely refer to it as an equity-like claim.When (5) does not hold, V C i offers γi e = R F , Π(V Ce)+I−(1−q(He)p)R F q(He)p , which pays proportionally more in case of failure, and can be replicated by a straight debt contract, but 13 Note that we do not consider equilibria in which VCs initially offer different menus following different signals: such equilibria would immediately reveal VCs' information to their rival and boil down to symmetric information Bertrand competition, reducing both VCs' expected profit to zero.VCs would then prefer either to coordinate on the equilibria presented in Proposition 1 or to implement a one-stage auction.
14 When condition (5) does not hold, the only equilibrium contract offered by V C i is γi e because this is also the entrepreneur's preferred contract: V C e cannot threaten to maintain a contract that is strictly preferred by the entrepreneur to γi e .
not by any equity-like claim.Last, when V C e finances the entrepreneur, he reaps all gains in all states of nature, which can be replicated by a 100% equity contract, or a debt contract with a large repayment.V C e 's claim is then indeterminate.
These equilibrium financial contracts arise because VCs have different levels of experience, and private information.When projects are particularly risky (R F is small), V C e is able to exploit his superior information and offers his preferred contract, that pays more in the success state.
When projects are less risky (R F is large), V C i can offer contracts that pay more in the failure state, which reduces V C e 's informational (and competitive) advantage.Finally, note that outside equity financing naturally emerges from our assumption on the venture capital industry.If all venture capitalists had the same level of experience, they would have the same preferences, and would be indifferent among financial contracts.Other analyses show that investors might prefer to acquire debt or equity according to the type of information they have (Inderst and Mueller (2006) or Habib and Johnsen (2000)).Our model is the first to derive outside debt or outside equity as an equilibrium feature of competition among investors.

The role of removable offers
Our choice to model competition with removable offers has a double advantage: firstly, it fits well with industry practice whereby term sheets are proposed but can be removed before final agreement.Secondly, it allows to obtain pure strategy equilibria which provide clear-cut results on the type of financial contracts offered at equilibrium.The existence of pure strategy equilibria relies on the same intuition as in Broecker (1990).The ability of VCs to withdraw offers alleviates the winner's curse which sustains pure strategies. 15If VCs cannot offer menus of removable offers, only mixed strategy equilibria prevail, as analyzed in the literature of auctions between asymmetrically informed bidders. 16nother important assumption of our competition game is that VCs can offer menus of contracts.
When condition (5) holds, this allows V C e to ultimately offer his preferred contract in the set Γ i .
This is only possible because V C e can offer several contracts in his initial menu.If instead V C e is restricted to offer a single contract (on top of the null contract), he cannot offer γe i any more because this contract triggers profitable deviations from V C i .To prevent such deviations, V C e is bound to offer the entrepreneur's preferred contract in Γ i , which reduces V C e 's equilibrium profits.

Exclusive talks
Suppose now that the entrepreneur can commit to a period of exclusive talks with one VC, denoted V C 1 , before trying to generate offers from another VC. 17We model exclusive talks as the following two-stage bargaining game.In the first stage, the entrepreneur bargains with V C 1 .The first stage is divided into an infinite number of time periods t (t = 0, 1, 2, 3, ...,).In each time period, the entrepreneur or V C 1 has the opportunity to move to a second stage by approaching the second VC, denoted V C 2 .In that case, the "shopping around" game described in section 4 starts.
The timing of the first stage is the following: 1.At t = 0, V C 1 makes an offer.The entrepreneur accepts the offer, or terminates exclusivity, or 2. At t = 1, the entrepreneur makes a counteroffer.V C 1 accepts the offer, or terminates exclusivity, or 3.At t = 2, V C 1 makes an offer, and the game continues as defined at t = 0.
The second stage starts if one agent terminates exclusivity.The exclusive talk stage is thus modeled as a standard Rubinstein bargaining game with an option to terminate exclusivity.The original feature of our modeling is that the value of the exit option is endogenous.It depends on the second stage competition between the two VCs.We also assume that there is some cost in delaying negotiation.Precisely, when agents agree on a contract γ 1 at time t during the first stage, the entrepreneur obtains: where β < 1 reflects entrepreneur's impatience. 18f one agent opts out at time t, the two agents obtain their outside option, i.e. their payoff in the shopping around stage.The key element to define these payoffs, and thus the issue of the exclusive talks period, is the belief that V C 2 assigns to the event that V C 1 has received a high signal when the game gets to the second stage.We assume that the entrepreneur cannot prove to V C 2 that he received a binding offer. 19Thus V C 2 faces an inference problem: He can be approached either because the first venture capitalist observed a low signal or because exclusive negotiation breaks down.Denote δ the probability that V C 2 assigns to the event that exclusive negotiation breaks down.When δ = 1, V C 2 's initial belief about the project quality is equal to q 0 , as in the shopping around game.When δ < 1, V C 2 is a priori more pessimistic about the project quality: being contacted after a period of exclusive talks is in itself a negative signal.This modifies V C 2 's equilibrium strategy and in turn, the entrepreneur's and V C 1 's outside option payoffs.The next propositions characterize admissible equilibria.
Proposition 2 There exists an equilibrium such that V C 1 makes an offer when s 1 = H and no offer when When δ = 0, an agreement with V C 1 occurs at t = 0 and exclusive negotiation succeeds.V C 2 believes that he is approached only when V C 1 has received a low signal, and that he faces no competing bid if he makes an offer.As a consequence, if V C 2 is V C e , his best response is to offer γ e = (R F , R S ) (monopoly offer), and if V C 2 is V C i , his best response is to offer the null contract, i.e. γ i = (0, 0).Because of V C 2 's best response, V C 1 can capture the project NPV at the second stage.The outside option of the entrepreneur at t = 0 reduces to βq(H 1 )pB and the outside option of V C 1 is N P V (H 1 ).In other words, the entrepreneur and V C 1 's outside options are their off the equilibrium path payoffs given V C 2 's belief that he is contacted only if s 1 = L.At the first stage, the entrepreneur and V C 1 both agree on a partition that leaves them at least their outside option.
Proposition 3 There is no equilibrium such that V C 1 makes an offer when s 1 = H and no offer when s 1 = L, and such that the entrepreneur terminates exclusivity with positive probability.
When δ > 0, V C 2 believes that exclusive negotiation breaks down at t = 0 with positive probability.An equilibrium with δ > 0 can only exist if the second signal is valuable enough so that the surplus shared between V C 1 and the entrepreneur is larger at the second stage than at the first stage.Intuitively, this can only happen if V C 2 is V C e .But, as illustrated in proposition 1, V C e is able to capture part of the project surplus thanks to his informational advantage.We show in the appendix that, because of V C e 's market power, the entrepreneur and V C 1 always have an incentive to negotiate at the first stage.For that reason, exclusive negotiation never fails in our setting, and equilibria with δ > 0 cannot be sustained.
Propositions 2 and 3 focus on separating equilibria (i.e.such that V C 1 makes a different offer when s 1 = H and when s 1 = L).It is useful to discuss whether pooling equilibria can also be sustained.Observe first that, given that the project initial NPV is negative, such equilibria cannot be sustained if first stage negotiation succeeds with positive probability.We must therefore have δ = 1 in which case the game boils down to the shopping around game.For that reason, we consider that these equilibria do not arise with exclusive talks.
Corollary 3 If the entrepreneur decides to initiate exclusive talks, he always approaches V C i first.
The intuition of corollary 3 is straightforward.The entrepreneur's expected utility under negotiation is simply his expected private benefit, which is maximized when he contacts V C i first, keeping a chance to be financed by V C e later if s i = L.20

Equilibrium negotiation strategy and empirical predictions
We first analyze which negotiation strategy is chosen by the entrepreneur in equilibrium.To do this, we compare the entrepreneur's expected utility in both games, and obtain the following proposition.
Proposition 4 The entrepreneur prefers to shop around if condition (5) does not hold, or if the level of private benefit B is not too large in the sense that: Otherwise, the entrepreneur prefers to engage in exclusive talks.
Proposition 4 implies that when the entrepreneur values mostly monetary profits, he prefers to shop around.The value of funded projects is larger, and the entrepreneur captures a large part of it thanks to competition.When the entrepreneur's private benefit becomes large, the entrepreneur cares more about the probability to obtain funding. 21When projects are riskier, that is when they have a lower cash flow R F , and therefore a higher variance (condition (5) holds), opting for exclusive talks guarantees that the entrepreneur is financed either when V C i has a high signal, or when V C e does.If he chooses instead to shop around, he only obtains financing when V C e has a high signal.He then prefers exclusive talks. 22When projects are less risky (in the sense that condition (5) does not hold), the entrepreneur has the same probability to obtain financing with the two negotiation strategies.He therefore prefers the one that gives him a higher monetary profit and always chooses to shop around.The following corollary explores the efficiency of the resulting investment.
Corollary 4 is immediate.When either (5) or ( 6) does not hold, V C i finances the entrepreneur with positive probability, while it is efficient to finance projects if and only if s e = H.
Our analysis helps to shed new light on the determinants of VCs' deals with entrepreneurs.In particular, we can derive new empirical predictions relating entrepreneurs' private benefit and project characteristics to VCs' portfolio attributes and equilibrium deals.We detail below these predictions, confront them to existing evidence and provide additional tests of our theoretical framework.

Predictions on VCs' portfolio characteristics
A first insight of our model is that VCs' deal flow (i.e. the number of investment offers they receive) results from the optimally chosen negotiation strategy of entrepreneurs.Our model predicts that the level of deal flow varies with the experience of VCs, the type of entrepreneurial projects, and the level of private benefit of entrepreneurs.We are not aware of empirical studies on VCs' deal flow, but our theory is consistent with the following empirical hypotheses: if one considers a population of entrepreneurs distributed according to their level of private benefit and project risk, an implication of the model is that inexperienced VCs should have a higher deal flow (controlling for fund size, strategy and specialization).Also, inexperienced VCs should attract more entrepreneurs with riskier projects and higher private benefits than experienced VCs.To test this second hypothesis, the empirical challenge is to measure the level of private benefit of entrepreneurs.One possibility is to interpret private benefits as future reputation gains if the venture succeeds.Success makes entrepreneurs more visible, increases their perceived talent, and expands the set of future job opportunities. 23Reputation gains (and private benefits) are thus likely to be higher for young entrepreneurs with no track record or media coverage.
We can also derive predictions regarding the type of financial contract offered to entrepreneurs.
Firstly, VCs are more likely to finance entrepreneurs with debt-like claims when projects are less risky (i.e. have a higher liquidation value, which corresponds to R F in the model) and when VCs are less experienced.Conversely, VCs are more likely to finance projects with equity-like claims when projects are riskier and VCs are more experienced.Importantly, the prediction on financial contracts issued at equilibrium results from the combination of the level of risk of projects and the level of experience of VCs.In particular, the model does not predict that less experienced VCs are more likely to acquire debt-like claims to finance risky projects.Last, entrepreneurs with lower private benefits should issue more equity-like claims.These predictions are partially supported by empirical evidence.For instance, Kaplan andStromberg (2003, 2004) do find that serial entrepreneurs are more likely to obtain liquidation rights, and have less performance-sensitive equity stakes, which is consistent with our prediction regarding low private benefit entrepreneurs.
The novelty of our analysis is to offer more precise predictions relating different VCs and entrepreneurs' attributes.The joint consideration of these attributes has, to our knowledge, not been tested so far.

Predictions on entrepreneurs' financing deals
A result of the model is that high private benefit entrepreneurs are more likely to engage in exclusive negotiation, to contact less experienced VCs, and to receive only one offer.Therefore, we expect first-time entrepreneurs to receive less offers on average than serial entrepreneurs, holding project risk constant.Another result of the model is that single offers are more likely to come from less experienced VCs. 24This second prediction is consistent with the empirical observations of Hsu (2004): the average level of experience of VCs is significantly lower when entrepreneurs receive a single offer, compared to when they receive several offers.Whether this effect prevails for high benefit entrepreneurs has not been tested.
We can also relate the average level of experience of VCs to projects' characteristics.When projects are riskier (i.e.R F is smaller), the entrepreneur is more likely to be financed by V C e . 25ast, at the exclusive negotiations equilibrium, VCs capture all monetary profits.This implies that pre-money valuations should be lower when entrepreneurs engage in exclusive talks, and receive only one offer at a time.This effect is documented by Hsu (2004) who finds that pre-money valuations are significantly lower in single offer deals than in multiple offer deals.The interest of our analysis is to explain why entrepreneurs optimally choose to relinquish bargaining power to VCs.

Robustness
In our model, we highlight the screening role of VCs by assuming that they have a costless information generation technology.In reality, information acquisition is costly, which may refrain VCs from engaging in investment analyses when their prospects of financing a deal are low.This effect can arise in our model.If we introduce costly signals, we cannot sustain equilibria in which one VC has a zero probability to finance the entrepreneur's project (because he cannot recoup the cost of his signal).In that case the equilibrium of the shopping around game is modified as follows: when condition (5) holds, the equilibrium is in mixed strategy only (see Milgrom andWeber (1983), von Thadden (2004) or Hauswald and Marquez (2003)) and is such that V C i provides financing with positive probability.In this equilibrium, both VCs make positive profits, and a costly signal does not impede their participation.Considering costly signals does not affect our other results since in all other equilibria, both VCs make positive profits.
Consider next the case in which VCs have to exert effort to improve the quality of their signal.If effort is continuous, then the first best levels of effort maximize total project surplus.With private information, the efficiency of the investment decision is less clearcut.In the shopping around game, V C e is not able to capture all profit, and underinvests in information acquisition.In the exclusive talks game, V C i captures all surplus, and may overinvest in information acquisition (because he is less experienced).
Also, considering that VCs can add value to the project after financing is realized can alter some of the results.In particular, in the exclusive talks game, the entrepreneur is less willing to ap-proach V C i first if we assume that VCs' experience increases the level of private benefit of the entrepreneur26 or the probability of success of the venture.In turn, the entrepreneur is less likely to engage in exclusive talks.

Conclusion
In this paper, we investigate how competition takes place in the venture capital industry, resulting from entrepreneurs' negotiation strategy.We consider a model whereby a cash-poor entrepreneur decides whether to propose his project to two VCs at the same time or to initiate negotiation with one VC first.The two VCs extract private information on the true value of the project, but have different signal precisions.In addition, the entrepreneur enjoys non monetary benefits when his project succeeds.When deciding his optimal negotiation strategy, he cares about expected monetary profits, and about the probability to get funded.
A first insight of the model is that because of asymmetric information among VCs, the latter can capture positive profits even if the entrepreneur approaches both at the same time.In that case, he can be financed by the more or the less experienced VC, depending on the level of risk of the project.In particular, riskier projects can only be financed by experienced VCs.Also, because they have different assessments of the projects, VCs have different preferences over which financial contracts to acquire: the experienced VC is more likely to buy equity, while the inexperienced VC prefers to acquire debt, retaining then more liquidation rights.Last, because of imperfect competition, the entrepreneur may prefer to commit to exclusive talks to increase the probability to obtain financing.This occurs when his private benefit is high.
The optimal negotiation strategy thus depends on the entrepreneur's private benefit and project's risk.The model predicts that more experienced VCs are more likely to finance riskier projects with equity-like claims.Also, high private benefit entrepreneurs are more likely to receive a single offer and to be financed by less experienced VCs.

Appendix
Proof of Lemma 1 Since q(H e ) > q(H i ), we obtain γe i = I−q(H i )pR S 1−q(H i )p , R S .The contract γi e is computed straightforwardly using the same procedure.

Proof of proposition 1
A strategy profile for V C α is a menu C α contingent on s α , and a decision to maintain an offer γ α in C α contingent on s α , and on his competitor's menu C −α .By assumption, (0, 0) ∈ C α .
Our equilibrium concept is Perfect Bayesian Equilibrium.
Let us solve the game backwards and determine the decision to maintain an offer.Observe first that it is a dominant strategy for any V C α to maintain (0, 0) after s α = L. Since N P V (H i , L e ) < 0, V C e optimally chooses (0, 0) when s e = L. Anticipating this, it is a dominant strategy for V C i to choose (0, 0) when A i represents the set of all contracts that V C i strictly prefers to any contract in Γ i when s is accepted with probability one.Define equivalently A e = {γ e ∈ [0, R F ] × [0, R S ] : q(H e )pR S e + (1 − q(H e )p)R F e > Π(V C e )} and A −e its complement.
1) Assume first that condition (5) holds, and define γE ) ∈ Γ i .The contract γE i maximizes the entrepreneur's utility in Γ i when he believes that s i = s e = H.27 Consider the following strategies.
i and the entrepreneur shows all offers.
We now show that these are equilibrium strategies.From our initial remark, any V C α maintains (0, 0) when Following such a deviation, V C i optimally maintains γE i .
2) Assume next that condition (5) does not hold.Observe that γi e defined in lemma 1 is also the entrepreneur's preferred contract in Γ e when he believes that s i = s e = H.Consider the following strategies.
• If s e = H, V C e maintains (R F , R S ) if C i = C * i . •

Proof of corollary 1
Suppose (5) holds.Consider an equilibrium in which C e includes γ e ∈ {A −i − Γ i } ∩ A e .We show that an equilibrium such that γ e is ultimately offered by V C e cannot be sustained.Consider V C e 's deviation C e that includes γ e = γ e + , with small enough so that γ e ∈ {A −i − Γ i }.To prevent this deviation, V C i must offer γ e in his menu, and maintain it following C e .The entrepreneur's choice is then to accept γ e , which yields negative expected profits for V C i .Therefore, γ e ∈ {A −i − Γ i } ∩ A e cannot be offered at equilibrium.Trivially, an equilibrium in which C e includes γ e ∈ A i along with contracts in Γ i cannot be sustained.Indeed, γ e is preferred by V C e if V C i maintains (0, 0), which induces V C i to deviate.
The same argument applies when condition (5) does not hold.
would always prefer to accept the offer.We show below that this necessary condition cannot be satisfied.
1) Assume that the entrepreneur contacts V C e first.The set of maximum bid contracts Γ i now depends on δ.The higher δ, the more confident V C i is about the project quality and about the occurrence of state R S .
Denote q(H i , δ) the probability that the quality of the project is good given that V C i has observed a high signal and given V C i 's belief δ, and N P V (H i , δ) the corresponding project value.Since N P V (H i , 0) < 0 and N P V (H i , 1) = N P V (H i ) > 0, there exists δ such that N P V (H i , δ) = 0.
Clearly, any equilibrium such that δ > 0 is such that δ ≥ δ (otherwise, V C i cannot make an offer, and there is no point in terminating exclusivity).Define Γ i (δ) and (R F (δ), R S (δ)) the intersection of Γ e and Γ i (δ).We know from Proposition 1 that if R F ≤ R F (δ), the equilibrium of the shopping game is such that V C e finances the entrepreneur if and only if s e = H.The surplus that the entrepreneur and V C e can share at the second stage is thus strictly smaller than N P V (H e ) + q(H e )pB because of the entrepreneur's impatience.This implies that V C e can always propose γ e such that he and the entrepreneur are both better off negotiating than going to the second stage.If R F > R F (δ), the second period equilibrium is such that V C i finances the entrepreneur if s i = H and V C e finances the entrepreneur otherwise.Because a rent must be left to V C i in this case, the joint surplus of the entrepreneur and V C e is strictly smaller than in the case in which R F ≤ R F (δ), and the above reasoning goes through.The equilibrium candidate in which δ > δ does not exist.
2) Assume next that the entrepreneur contacts V C i first.Their first stage surplus is: N P V (H i ) + q(H i )pB.
Define Γ e (δ) the set of contracts such that V C e is indifferent between offering a competitive bid, and offering the monopoly contract.Define now R F (δ) as the intersection of Γ e (δ) and Γ i .If R F ≤ R F (δ), we know from Proposition 1 that V C e offers γe i = I−q(H i )pR S 1−q(H i )p , R S and finances the entrepreneur if and only if s e = H.The second stage expected surplus of the entrepreneur and V C i is thus βP r(H e |H i ) q(H e , H i )p(R S − R S + B) + (1 − q(H e , H i )p)(R F − I − q(H i )pR S 1 − q(H i )p ) = βP r(H e |H i ) q(H e , H i )pB + 1 − q(H e , H i )p 1 − q(H i )p N P V (H i ) < N P V (H i ) + q(H i )pB.
If R F > R F (δ), we know from Proposition 1 that V C i offers γi e (δ) and finances the entrepreneur with probability one (since s i = H).The surplus that the entrepreneur and V C i can share is thus the same at the two stages (and equal to N P V (H i ) + q(H i )pB).Given the entrepreneur's impatience, they prefer to negotiate at the first stage, and no equilibrium with δ > 0 exists.
yielding negative expected profits for V C i .Last, when s e = H, V C e cannot profitably deviate either.First, given lemma 1, γe i maximizes V C e 's expected profit in C * e .Consider next a profitable deviation γ e by V C e .We necessarily have that γ e ∈ A i .
he is indifferent between maintaining (0, 0) and γE i (given V C e 's equilibrium strategy to maintain γe i if s e = H).We therefore postulate that, on the equilibrium path, V C i removes his offer.28Considernext V C i 's deviation γ i ∈ A i , such that the entrepreneur strictly prefers γ i to γe i when he believes that s i = s e = H.Following this deviation, V C e optimally maintains γE i , which is preferred by the entrepreneur to any contract γ i ∈ A i .The deviation γ i is then only accepted when s e = L, If s i = H, V C i maintains γi e if C e = C * e .Following the same argument as before, when s e = H, if V C e observes C * i , he weakly prefers to maintain (R F , R S ). 29 In addition, V C e cannot profitably deviate from C * e if he anticipates C * i .Indeed, V C i maintains γi e when s i = H, which is preferred by the entrepreneur to any contract γ e ∈ A e , given the entrepreneur's equilibrium belief that non null contracts are only maintained after high signals.Therefore, any deviation from V C e in A e is only accepted when s i = L, which reduces V C e 's expected profit.When s i = H, V C i cannot profitably deviate either.Choosing γe i in the menu C * i maximizes V C i 's expected profit given lemma 1.Also, following any profitable deviation by V C i , V C e optimally maintains γi e .