Working Paper. R&D and market entry timing with incomplete information

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1 - preliminary and incomplete, please do not cite - Working Paper R&D and market entry timing with incomplete information Andreas Frick Heidrun C. Hoppe-Wewetzer Georgios Katsenos June 28, 2016 Abstract We study a model of R&D and market entry timing in which firms face incomplete information about the rivals R&D ability. First, the firms decide whether to invest in competing R&D projects, and second, if they invest, when to bring the new product on the market. We show that the observability of the R&D activity does not change the R&D investment decisions of the competitors. However without observable R&D decisions, the aggregate industry profit can be lower. Keywords: Innovation, First-Mover Advantage, R&D, Private Information. JEL Numbers: D82; O31 Financial support from the German Research Foundation (DFG), HO 3814/1-1, is gratefully acknowledged. Department of Economics, University of Hannover, Koenigsworther Platz 1, Hannover, Germany. 1

2 1 Introduction In 2003 the Boeing Company announced to start the development of a new longrange, twin-engine jet airliner. Boeing s competitor Airbus SAS also initiated a similar project. First, Boeing launched the Boeing 787 Dreamliner in Only in 2014, Airbus introduced the Airbus A350 XWB. Until 2015 Boeing delivered 363 units while Airbus supplied 15 airliners. 1 Also, the higher number of orders underline the market leadership of Boeing in this sector. In this case, Airbus and Boeing knew about the presence of the competitor while making the R&D investment decision. In contrast, in the financial market, investment banks conceal usually the development of innovative derivative securities. Herrera and Schroth (2003) show that the innovator of a new financial product has an informational first-mover advantage which turns the innovator into the market leader. The investment banks compete in a manner similar to that innovation competition of Airbus and Boeing, i.e., the innovator has a first-mover advantage if it markets the new product before its rival can complete its prototype. A natural question is whether firms make different R&D investments and market launch decisions if they can observe the rival s R&D activity. This paper considers a stylized model of R&D and market entry timing to aim the effect of observable R&D investments in such kind of innovation competition with first-mover advantage. Two competitors who face incomplete information about the rival s R&D ability decide whether to invest in R&D which results in a prototype for a new product. The firm who is first in completing a prototype receives a positive return from market entry as long as no rival firm has completed a prototype. Our analysis focuses on the incentives to improve the new product 1 The purchase order reports are available online by the companies, see Boeing (2015) and Airbus (2015). 2

3 further over time before the market is entered. While this increases the firm s returns from market entry, the firm risks to lose it s first-mover advantage when a rival prototype is announced. Our main result is as follows: Firms invests in the R&D project following a threshold rule. The observability of the rival s investment does not effect the R&D decision. With observability, firms choose a market entry date depending on the observation of the rival s R&D activity. Without this information, the market launches are derived from the probability of an investing competitor. In this case, low profit outcomes can occur. Close to our work is the paper by Botcheff and Mariotti (2012) who consider a model in which two potential players randomly and secretly arrive into the innovation game. These dates of birth are not observable for the respective competitor. In all equilibria each player s stopping time follows the same distribution. Firms are restricted to move only after their births. We also include this restriction in our setting with implementing the prototype dates. Hopenhayn and Squintani (2016) insert the same key feature in their sequential model of patent races. Firms cannot act unless they receive a breakthrough in the R&D activity which is exponentially distributed. Afterwards, while the innovation is improving deterministically, a firm can decide to patent its innovation which ends the current race. Hopenhayn and Squintani show that there exists a unique symmetric equilibrium in which firms decide to wait a constant duration after experiencing a breakthrough. In contrast to these models, we extend the strategy space of firms by introducing as the first stage the initial decision whether to enter the innovation competition or not. This feature represents the ability of firms to reject a project if the quality is not good enough, e.g., a R&D project with a late expected date of completion can be rejected to avoid a nonprofitable investment. The present paper does not include uncertainty about the value of the innovation, unlike in Hoppe (2000) or Jensen (1992). Both implement a stochastic uncertainty 3

4 about the value of the innovation. With a commonly known probability the innovation is good and firms gain a higher payoff. Hoppe shows that, conditional on the probability, in the equilibrium either the payoffs equalize (high probability) or informational spillover generate a second-mover advantage. In this paper, uncertainty is not included in that matter due to prevent creating a basis for second-mover advantage which does not suit in our contest situation. In the case of unobservable investments, we include uncertainty about presence of competitors in the second stage, like Hendricks (1992). Hendricks extends the model of new technology adoption of Fudenberg and Tirole (1985) by introducing asymmetry across firms. In particular, the private innovative capabilities of the competing firms can differ. A firm with low capabilities can be constrained to be an imitator. Otherwise, a high value firm can act like an innovator and adopts a new technology at any time. Hendricks derives a reputational equilibrium in which firms delay adoption to pretend to be an imitator. This mechanism reduces the rent dissipation in the context of Fudenberg and Tirole s setting. Following Hendricks, in our model firms prototype dates are fixed at the beginning of the innovation game. Firms can not observe the rival s prototype date. Finally, Moscarini and Squintani (2010) analyze a winner-takes-it-all R&D race between two firms. Firms receive a private signal about the arrival rate of the invention. Waiting for the invention arrival causes cost. Like to the present paper, only the winner gains the payoff, unlike to us, its payoff could be below the cost of the winner. Moscarini and Squintani identify a herding effect in the equilibrium. Our paper is organized as follows. We describe the model in Section 2. Section 3 presents the equilibrium analysis for each information setting. Also, in Section 3 we prove that the investment decisions follow a threshold rule. Section 4 concludes. 4

5 2 The Model There are two firms, i = 1, 2, engaging in R&D projects that aim, first, at the development of a prototype, and subsequently, at the introduction of a market product. The two projects are directly competitive: the creation of a prototype by one firm before a rival prototype comes into existence eliminates all possible profit for the other firm. That is, the reward structure for innovative activity has a winner-takes-all form. At the beginning, each firm i decides whether to invest in R&D, for a fixed cost K > 0, or to exit the game, for a payoff of zero. The two firms differ in their R&D abilities, with each firm being characterized by its earliest possible date of creating a prototype, denoted by T i. The variable T i is private information of firm i and is independently and identically distributed on the interval [0, 1], according to the uniform distribution. Following the development of a prototype, i.e., at any date t T i, firm i chooses whether to bring the new product to the market. 2 If market entry occurs before the rival firm has created a prototype, i.e., at time t < T j, firm i obtains a market profit L (t),whereas firm j obtains a zero payoff. By delaying entry, firm i can improve its new product over time or wait for better market conditions, yielding a higher first-mover advantage. More precisely, we assume that L(t) is twice continuously differentiable, strictly increasing and strictly concave on [0, 1], with L (0) = 0. On the other hand, if firm i enters the market after firm j has already created a prototype, i.e., at time t T j, then we assume that firm j follows suit immediately such that both firms obtain the same payoff M. In order to simplify the exposition 2 This is similar to the random arrival dates of players in the innovation timing games by Bobtcheff and Mariotti (2012) and Hopenhayn and Squintani (2016). In contrast to these models, we allow firms initially to decide whether to enter the innovation competition or not. 5

6 we assume that M = 0. That is, the new product provides an advantage for the first entrant only when the rival firm has not created a prototype. Once both prototypes are completed, the possibility of firms to immediately respond to their rival s market entry completely eliminates the first-mover advantage. 3 We distinguish between two different information settings. First, the firms can observe one another s initial R&D investment decision. Second, the initial R&D decision of each firm remains its private information, so that the firms face uncertainty about the presence of a competitor in the subsequent innovation game. Finally, each firm is risk-neutral, so that its payoff is either zero or its expected market profit minus the R&D cost. The equilibrium concept is that of perfect Bayesian equilibrium. 3 Equilibrium analysis We focus on symmetric equilibria in pure strategies. First, we examine firm i s choice of the time t, for t T i, to enter the market, following investment in R&D; and subsequently, we determine the prototype times T i for which firm i is willing to invest. As it turns out, for any strategy of firm j, the best response of firm i takes the form of a threshold rule, characterized by some cutoff type Z i, for the firm s initial R&D investment decision: 3 Note that, we implicitly use the tie-breaking rule that if a firm is indifferent between market entry as a follower and exiting the game, the firm enters the market. This structure captures settings in which firms that have already developed a prototype, find it more profitable to introduce their new product to the market than exit. 6

7 invest in R&D whenever T i Z i ; otherwise do not invest. Indeed, for any prototype times T i < T i, if the type T i of firm i adopts the same strategy as the type T i, then it will achieve the same profit. Thus, if the type T i can derive a positive payoff from investing in R&D, then the type T i is also able to do so; and therefore, it will be better off investing. Following this observation, we can restrict our analysis to strategies with a threshold rule for the firms initial R&D investment decisions. 3.1 Observable R&D investments We assume here that firms can observe the R&D investment decision of their rival before they decide when to enter the market. In the next subsection we will focus on the case of private R&D investments. Regarding the R&D history, we need to distinguish between two cases: I denotes the history in which only firm i has invested in R&D, and B denotes the history in which both firms have invested in R&D. Obviously, when firm j has not invested in R&D, firm i will choose to enter the market at the time at which the market-profit curve L(t) attains its maximum, i.e. t = 1. Firm i s expected payoff is then πi I = L (1) K. Next, suppose that firm j has invested in R&D. In this case, firm i can gain a positive payoff if and only if it enter the market before its opponent has completed a prototype, i.e., at any time t i < T j. Firm i s expected payoff in the entry timing 7

8 stage is then π B i (t i ) = Pr (t i < T j T j Z j ) L (t i ) K = Z j t i Z j L (t i ) K, (1) for t i [T i, Z j ] and T i < Z j. Note that, if firm i observes that the rival invests and T i Z j, firm i gains a zero payoff at any possible entry time t T i since T i > T j. The first-order condition of (1) is L (t i ) Z j t i Z j L (t i) Z j = 0 L (t i ) = 1 Z j t i L (t i ). (2) It is easy to show that equation (2) has a unique solution ˆt i (0, Z j ). Notice that L is positive and strictly decreasing over (0, Z j ], with L (0) > 0, while the RHS of (2) is positive and strictly increasing over (0, Z j ], with L (0) = 0 and lim ti Z j 1 Z j t i =. Therefore, the two curves cross exactly once. At time ˆt i, the marginal benefit of a later entry date, i.e., L (t i ), equals the corresponding expected marginal loss, i.e., the probability that firm j finishes its prototype in the next instant, conditional on not having finished yet, multiplied by the foregone benefit L (t i ). The concavity of the profit function and the presence of the rival avoid any incentives to deviate to any later date. For T i > ˆt i, however, the prototype constraint is binding. 4 Thus, firm i s optimal entry time is given by t i = max {ˆt i, T i }. (3) We now turn to the analysis of the firms R&D investments. Note that firm i will invest in R&D if and only if its expected payoff in the subsequent game is nonnegative. Given that firm j follows a threshold strategy, characterized by the 4 See Appendix: Figure 1 illustrates the optimal market entry timing of firm i. 8

9 cutoff Z j, firm i s expected payoff from investing in R&D is Pr (T j Z j ) πi B (t i ) + Pr (T j > Z j ) [L (1) K] if T i < Z j Π i (T i ) = Pr (T j > Z j ) L (1) K if T i Z j. Note that the payoff Π i (T i ) is constant for T i ˆt i ; strictly decreasing for ˆt i < T i < Z j ; and constant again for T i Z j. In addition, notice that Π i (T i ) is continuous. Hence, if Π i (T i ) < 0 for T i ˆt i, firm i does not invest in R&D; if Π i (T i ) > 0 for T i Z j, firm i does invest; and for ˆt i < T i < Z j, there exists a unique Z i, defined by Π i (Z i ) = 0 such that firm i invests in the project if and only if T i Z i. When the firms follow symmetric strategies, i.e., Z = Z i = Z j, we have Π i (Z) = 0 (1 Z) L (1) K = 0 (4) Z = 1 K L (1) In this case, the R&D investment strategy of firm i, as characterized by the cutoff rule invest in R&D whenever T i Z; otherwise do not invest; for i = 1, 2,where Z is given by (5), along with its subsequent optimal entry time, forms a best response to the strategy of the other firm, characterized by the same cutoff rule. We conclude the following proposition: (5) Proposition 1 Suppose the R&D investments are observable. Then there exists a symmetric equilibrium in threshold strategies with the cutoff Z, as given by (5). For T i Z, the equilibrium involves entry at t i = 1 if firm j i has not invested in R&D; and entry at t i = t i otherwise, where t i is defined by (3). 9

10 3.2 Unobservable R&D investments Assume now that the R&D investments in the first stage of the game are not observable. Suppose that firm j employs a strategy characterized by the cutoff Z j. Firm i s expected payoff from delaying entry until date 1 in the subsequent entry game, is then π i (1) = Pr (T j > Z j ) L (1) K = (1 Z j ) L (1) K For any other entry time, firm i obtains a positive profit L(t i ) if and only if either t i < T j Z j, i.e., firm j has invested in R&D but not developed its prototype, or T j > Z j, i.e., firm j has not invested in R&D. Firm i s expected payoff is then π i (t i ) = [Pr (T j Z j ) Pr (t i < T j T j Z j ) + Pr (T j > Z j )] L (t i ) K [ ] Zj (Z j t i ) = + (1 Z j ) L (t i ) K Z j = (1 t i ) L (t i ) K. (6) The first-order condition is L (t i ) (1 t i ) L (t i ) = 0 (7) L (t i ) = 1 1 t i L (t i ). (8) An argument identical to the one used in equation (2) shows that equation (8) has a unique solution t i. Note that in the case of private R&D, the probability that firm j finishes its prototype during the next instant, conditional on not having finished yet, is lower compared to the corresponding probability in the observable case. This implies that t i ˆt i, that is, firm i has an incentive to enter the market later if it is uncertain about the presence of the rival. Clearly, for firm i to be able to enter at t i, its type must be T i t i. Thus, by concavity π i (t i ) is maximzed by t i = max { t i, T i }. (9) 10

11 A comparison of the two expected payoffs results in π i (1) > π i (t i ) (1 Z j ) L (1) K > (1 t i Z j < 1 (1 t i ) L (t i ) K ) L (t i ) L (1). (10) That is, if the probability of an active rival j, Z j, is sufficiently small, then firm i will optimally delay its market entry until 1. Otherwise, the optimal entry date is t i. Next, to analyze firm i s R&D investment choice, notice that its expected payoff π i (t i ) from stopping at time t i, given by equations (6) and (9), is decreasing in the firm s prototype date T i. Therefore, firm i s optimal payoff from investing, Π i (T i ) = max{π(1), π i (t i )}, is also decreasing in the firm s prototype date T i. It follows that there exists a threshold time Z i such that firm i will invest in R&D for a positive expected payoff, if T i < Z i ; and stay out of the game, otherwise. 5 Finally, to derive a symmetric equilibrium, with an investment threshold Z, notice that the threshold type T i = Z will derive positive market profit if and only if the rival firm has not invested itself in R&D. Therefore, the threshold type will be best-off stopping at t i = 1. Requiring that the payoff of that type is zero, for the 5 Notice that Z i = 0, when Π(0) 0, in particular, when K L(1); and that Z i = 1, when Π(1) 0, in particular, when K = 0. 11

12 threshold condition, yields Π i (Z) = Pr (T j > Z) L (1) K = 0 (1 Z) L (1) K = 0 Z = 1 K L (1). (11) It is interesting to notice that the expected payoff Π i (Z) is independent of the prototype time T i ; i.e., if firm j invests according to the cutoff Z, then all types of firm i can derive zero expected payoff from investing in R&D and stopping at t i = 1, with some types being able to derive strictly positive payoff from stopping earlier. In particular, all types T i > Z of firm i are indifferent between investing in R&D and staying out; therefore, to derive an equilibrium, we assume that they stay out. Proposition 2 Suppose the R&D investments are unobservable. Then there exists a symmetric equilibrium in threshold strategies with the cutoff Z, as given by (11). For T i Z, the equilibrium involves entry at t i = 1 if π i (1) > π i (t i ); and entry at t i = t i otherwise, where t i is defined by (9). 4 Concluding remarks In this paper, we have investigated the impact of observability of investments in R&D projects in a direct competition of two firms. We characterized the conditions of each firm s investment decision and market launch and exhibited a pure-strategy equilibrium. In particular, we found that a firm s investment decision is independent of the observability of the rival s investment. Each firm invests following a threshold rule Z, i.e., it invests if its prototype completion date is not later than Z. This threshold depends on the ratio of the R&D cost and the maximum market 12

13 profit which the firms can gain. Higher cost implies a more restrictive threshold, so that fewer firms will be willing to engage in R&D. Investing firms occur with the same distribution and therefore, the aggregate R&D costs are also identical distributed. Thus, the issue of observability does not effect the efficiency of the firms R&D decisions. In contrast, the market launch decisions are affected by the observability of the firms investments. Observing that the rival has not invested allows a firm to delay the market launch until it can find the best possible market condition, i.e., until t = 1. Otherwise, after observing the rival invests, a firm enters the market immediately at the prototype date or delays the market entry only for a short time, to t. The sunk R&D cost is irrelevant for the market launch decision. In the case of unobservable investments, a firm considers the probability of an investing rival, which depends on the threshold and therefore on the R&D cost. This leads to two significant distinctions in the market launch of the firms compared to the observable setting. First, when the R&D cost is high, any firm that may invest will attempt to delay the introduction of its market product until t = 1, a market launch strategy that can lead to low profit outcomes for the industry, if the rival also invests. And second, when the R&D cost is relatively low, so that the probability of the rival firm investing is high, a firm may launch its product too early, for an efficient market outcome. These results suggest that firms in direct competition can benefit from disclosing their R&D investments. Although, the observability does not effect the investment decisions, it allows for more profitable or more efficient market launches. Hence, in the case of Airbus and Boeing, the firms decisions to disclose their R&D investments can be justified as an effort to achieve a more profitable market outcome. While the results of our model are driven by the stylized payoff structure, i.e., 13

14 any market advantage is eliminated when the rivals prototype is complete, further research might relax this assumption. Relaxing the complete elimination can reduce the loss from suboptimal outcomes. One can extend this work, by considering more general information and payoff setting. In addition one can consider the possibility of endogenous disclosure decisions. Indeed, it will be interesting to analyze the reasons for which a firm that can choose to conceal its investment decision will decide instead to disclose it to its opponent. This question is the subject of current research. 14

15 Appendix Case I: Observable R&D investment Figure 1: Entering decision of firm i t 1 Z j ˆt i ˆt i Zj 1 T i Remark: The horizontal axis represents the prototype dates and the vertical axis shows entering time. The green curve is the optimal entering time if the rival does not invest in R&D, and the red curve describes the decision plan if the competitor invests. Case II: Unobservable R&D investment Figure 2: Entering decision of firm i t 1 t i t i Z j 1 T i Remark: The horizontal axis represents the prototype dates and the vertical axis shows entering time. The green curve is the optimal entering time if threshold of the rival is Z j < 1 (1 t i ) L(t i ) L(1), and the red curve describes the decision plan if the presence of a competitor is more likely. 15

16 Numerical examples L(t) t 1 (t 1) 2 Z 1 K 1 K t i observable investments 1, if a j = 0 1, if a j = 0 max { Z, T 3 i}, if aj = 1 K unobservable investments ( 2 3 9, 1 ] max { 2Z, T 3 i}, if aj = 1 K ( 8 27, 1] t i 1 1 [ ] K 0, K [ 0, 8 27 t i 1 3, T i, 1 2 3, T i, 1 ] 16

17 References [1] Airbus SAS, ( ). [2] Benoit, J.-P., Innovation and Imitation in a Duopoly. Review of Economics Studies, Vol. 52, pp [3] Bobtcheff, C. and Mariotti, T., Potential competition in preemption games. Games and Economic Behavior, Vol. 75, pp [4] Boeing Company, ( ). [5] Fudenberg, D. and Tirole, J., Premption and Rent Equalization in the Adoption of New Technology. Review of Economic Studies, Vol. 52, pp [6] Hendricks, K., Reputations in the adoption of new technology. International Journal of Industrial Organization, Vol. 10, pp [7] Herrera, H. and Schroth, E., Profitable Innovation Without Patent Protection: The Case of Derivatives, FAME Research Paper No. 76. [8] Hopenhayn, H.A. and Squintani, Patent Rights and Innovation Disclosure. Review of Economic Studies, Vol. 83, p [9] Hopenhayn, H.A. and Squintani, Preemption Games with Private Information. Review of Economic Studies, Vol. 78, pp [10] Hoppe, H.C., Second-mover advantages in the strategic adoption of new technology under uncertainty. International Journal of Industrial Organization, Vol. 18, pp

18 [11] Jensen, R., Adoption and diffusion of an innovation of uncertain probability. Journal of Economic Theory, Vol. 27, pp [12] Moscarini, G. and Squintani, F., Competitive experimentation with private information: The survivors curse. Journal of Economic Theory, Vol. 145, pp [13] Reinganum, J.F., Uncertain Innovation and the Persistence of Monopoly. The American Economic Review, Vol. 73, pp