Abstract
In this paper, we develop a theoretical framework to investigate the impact of adopting a strategy of know-how trading on the degree of research and development (R&D) cooperation. We show that the consequences of cooperation in know-how sharing under the conditions of the model are similar to a policy of cooperation in R&D investments in areas with large spillovers. An industry-wide policy of cooperation among competitors with respect to R&D investment and sharing would simply result in maximal joint profits. This cooperative R&D outcome could be generalized to any degree of spillover other than 100%. In this paper, the commitment to a policy of know-how trading by the participants in an industry is explained by the firm’s attempt to induce the equilibrium of a single industry-wide cooperative research joint venture. In a repeated game framework, we show that pre-commitments by non-cooperative firms to disclose their own know-how to the industry can be effective in inducing cooperative R&D investments by the participants.
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Appendix
Appendix
Here we deduce the critical value of the discount rate. The formal analysis of repeated games with an infinite horizon applies the firm’s discount factor R to the firm’s expected cash flow in any period. Formally, this discount factor is equal to \( R=\frac{1}{1+r} \), where r is the discount rate for a given time period.
Suppose that we have two firms in a market that wish to cooperate in R&D. Let \( {\pi}_i^M \) denote the profit each firm earns if each firm cooperates in R&D, \( {\pi}_i^D \) the defection profit for firm i, and \( {\pi}_i^N \) the non-cooperative Nash equilibrium profit. The general result is that cheating on the cooperative arrangement does not pay provided that the discount factor is such that
In our game, after replacing \( {\pi}_i^D \), \( {\pi}_i^M \), and \( {\pi}_i^N \) with \( \frac{{\left(a-A\right)}^2\gamma {\left(9\gamma -4\right)}^2}{{\left(9\gamma -8\right)}^3} \), \( \frac{{\left(a-A\right)}^2\gamma }{9\gamma -8} \), and \( \frac{{\left(a-A\right)}^2\gamma \left(9\gamma -8\right)}{{\left(9\gamma -4\right)}^2} \), respectively, in (11), we obtain, after simplifications,
The right-hand side of inequality (12) is the critical value of the discount factor. It takes on values strictly between zero and one, as the second-order condition for a maximum with respect to the R&D investment level in the non-cooperative case is satisfied for \( \gamma >\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$9$}\right. \). Hence, using the discount factor formula above, the critical value of the discount rate in our game is \( {\left(\frac{9\gamma -8}{9\gamma -4}\right)}^2 \).
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Da Silva, M.A.P.M. Cooperative R&D and Commitment to A Policy of Know-how Trading. Int Adv Econ Res 24, 123–133 (2018). https://doi.org/10.1007/s11294-018-9683-y
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DOI: https://doi.org/10.1007/s11294-018-9683-y