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We take a differential game approach to study the optimal choices of managerial firms concerning efforts in product a process innovation. We find the Nash equilibria under the open-loop and closed-loop information structure, and we compare the steady state allocations with the corresponding equilibria of markets populated by standard profit-maximising firms. We find that the managerial incentive leads firm to underinvest in product differentiation and to overinvest in process innovation, as compared to standard profit-maximising firms.

R&D activities and incentives, together with the pace of the resulting technical progress, have been core issues ever since the pioneering work of Schumpeter (1942) and the consequent debate about the so-called Schumpeterian hypothesis, according to which the higher is the degree of market power enjoyed by a firm, the higher is her incentive to invest in innovation. This debate has received a crucial impulse by Arrow (1962), putting forward convincing argument against the Schumpeterian claim, by pointing out that a firm operating initially under perfect competition should indeed be endowed with the highest possible incentive to strive for an innovation whereby, if successful, she could throw her rivals out of the market and acquire monopoly power over the latter.

In this paper we take a close look at those strategic incentives arising in a situation where firms share the costs and profits in a multi-firm project, and bargain for their respective (precommitted) split of cost- and profit-shares. We establish that, when each firm's effort contribution to the joint undertaking is mutually observable (which is often the case in closely collaborative operations) and hence can form basis of the contingent cost- and profit-sharing scheme, it is not the gross economic efficiency but the super-/sub-additivity of the nett returns from effort that directly affects the sustainability of a profile of firms' effort contributions. The (in)efficiency result we obtain in this paper is of different nature from so-called “free riding” or “team competition” problems: the set of sustainable outcomes with bargaining over precommitted cost- and profit-shares is generally neither a superset nor a subset of the sustainable set without bargaining.

The literature on R&D races suggests that noncolluding firms invest excessively in R&D. We show that this result depends critically on the winner-take-all assumption. Although rents continue to be dissipated once the winner-take-all assumption is relaxed because firms in general fail to provide the optimal R&D effort, the mechanisms behind this rent dissipation change with the degree of patent protection. We then illustrate how the patent system can be used to elicit the optimal R&D effort.