Theory and Methodology
Firms' R&D decisions under incomplete information

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Abstract

The paper considers a patent race in which firms do not know their relative positions. In this setting, firms that start in the same position proceed at the highest possible speed; and if one firm has an initial advantage it preempts the rival, but at the cost of dissipating a significant part of its monopoly rent. So the paper shows that incomplete information in a patent race leads to rent dissipation. The latter is higher, the higher the value of the prize and the lower the cost of R&D. Thus, for innovations that provide relatively high profits the time to discovery is shortened, but the social losses are likely to be high, due to duplication of effort.

Introduction

Very often the R&D activity that leads to the production of knowledge assumes the characteristics of a race between competing firms. If there is a perfect patent system, the winner takes all and the losers get nothing. On the other hand, if patent protection is imperfect, losers too may benefit from the innovation.

Among the authors who have analyzed models of patent race are Loury, 1979, Dasgupta and Stiglitz, 1980, Reinganum, 1981, Fudenberg et al., 1983, Harris and Vickers, 1985, Harris and Vickers, 1987, Beath et al., 1989 and Nti (1997). All assume that firms interact strategically and posit winner-takes-all games.

Although they differ in the characterization of the R&D game (Reinganum (1981) assumes that each firm chooses a time path of R&D expenditure at the outset, whereas Fudenberg et al. (1983) and Harris and Vickers, 1985, Harris and Vickers, 1987 assume firms revise their decisions according to their relative position in the race), all these models posit that each firm knows its relative position in the race, in terms of acquired knowledge.

Looking at the real world, however, it is very hard to maintain such an assumption. In competitive R&D markets, research programs are conducted secretly, and competitors know very little about the research progress of rivals until someone gets the patent. On the other hand, the imperfect information condition in which R&D activity takes place motivates many actions, ranging from industrial espionage to bluffing (overstating their successes in order to induce competitors to drop out of the race).

The aim of the present paper is to analyze a duopoly R&D game when firms do not know their relative positions. More precisely, in a framework with no uncertainty in R&D activity, we consider a duopoly model of patent race, in which the two firms compete for a prize of known value. Although they know their starting positions, they cannot monitor their rival’s progress.

In this framework we compute the Nash equilibria of the patent race in relation to the entire parametric space of the game and the initial positions of the firms.

The main conclusion is that both firms will engage in R&D if they are in the same position at the outset. In this case the firms dissipate the rent arising from the patent in the attempt to win the race. On the other hand, if they start in different positions only one firm engages in R&D, although the winner of the race dissipates a significant part of the monopoly rent in order to keep its rival from entering. Thus, the main implication is that in patent races incomplete information leads to rent dissipation.

By contrast, in the models cited if one firm gets a lead on its rival the latter drops out; the race turns out into a monopoly.

On the other hand, one feature of the above models is their inability to explain simultaneous discovery. Even “when firms begin with equal experience there is a burst of R&D followed by the eventual emergence of a monopolist” (Fudenberg et al., 1983, p. 15).

As a matter of fact, in many circumstances several firms make the discovery simultaneously (see Jewkes et al., 1969), as a result of research conducted in parallel and pursuing the same end.

Simultaneous discovery arises in a natural way when firms involved in a deterministic patent race have incomplete information about the position of their rivals. This is due to the fact that competitive firms conducting R&D activity in secret pursue research programs right up to the end of the race, so that if they pursue the same aim, firms that start in the same position get to the end discovery at the same time.

The paper is organized as follows. Section 2 presents the main features of the model, Section 3 computes the Nash equilibrium of the symmetric game, and Section 4 extends the analysis to an initial asymmetric position. Section 5 summarizes the main results.

Section snippets

The model

We consider a model in which two firms compete in a multistage patent race for the acquisition of a prize of positive value, V, common to both firms. Like Fudenberg et al. (1983), we assume that the competition is staged in discrete time t=0,1,…, and the discovery occurs with certainty when a given number of “units of knowledge”, N, are accumulated. The patent is awarded to the firm that first achieves level N. If both firms achieve the discovery simultaneously, the prize goes to the firm with

The Nash equilibria of the symmetric game

The aim of the present section is to establish the conditions under which the Nash equilibrium exists, assuming that the firms start the race in the same position. We consider the case in which firms start in different positions in the following section.

Let us first prove two useful lemmas. The first establishes that provided one firm is the winner of the race it is profitable for it to make the lowest effort necessary to achieve the discovery. In formal terms, we have

Lemma 1

If kN=m>k=0, thenUi(Sk,S*

The asymmetric game

We now consider a situation in which one firm has an advantage over the other firm at the beginning of the race, due to such factors as differences in size, market position or assets, and this advantage is common knowledge to both.

Let us assume at the outset that firm i is k⩾1 steps ahead of firm j,i,j=a,b. That is, firm i needs to accumulate only Nk>0 units of knowledge when j must accumulate N units to get to the discovery. The following theorem then holds.

Theorem 3

If firm i is k⩾1 steps ahead of firm

Conclusions

We have considered a deterministic model of a patent race, in which firms know their initial position but are not able to monitor the progress made by their rival. In this framework, we study the nature of the R&D race in relation to the position of the firms and the values of the parameters.

With respect to position, we have proved that firms that start in the same position get the discovery simultaneously, while an initial lead is enough to ensure the patent to the firm with the head start.

Acknowledgements

We are grateful to Vincenzo Denicolò and three anonymous referees for helpful comments on a previous version of this paper.

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