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Journal of Economic Interaction and Coordination

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15.01.2021 | Regular Article

On optimal regimes of knowledge exchange: a model of recombinant growth and firm networks

verfasst von: Ivan Savin

Erschienen in: Journal of Economic Interaction and Coordination | Ausgabe 3/2021

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Abstract

The literature has documented two patterns of knowledge exchange: free sharing of knowledge and barter exchange. The former has been coined as collective invention, while the latter is observed in the form of R&D alliance. This study, for the first time, compares these two modes of cooperation in creating and diffusing new knowledge. Doing so, we take seriously the network character of knowledge and the skewed distribution of innovation size by proposing a novel model. In this model, knowledge is represented by distinct letters and words constructed thereof and accumulated by agents over time. Discovering new words agents recombine available knowledge pieces not randomly but following certain ideas, semi-definite structures on what words can be further constructed. We proceed by allocating agents in a network and allowing them to cooperate over direct ties either in a regime of collective invention or bilateral R&D alliances. We find networks with skewed degree distribution as most productive under R&D alliances and perfect IPR since they best concentrate scarce resources in discovering different knowledge combinations. In contrast, under collective invention and imperfect IPR, clustered networks better diffuse valuable ideas and knowledge resulting in the overall superior performance. Furthermore, under imperfect IPR, collective invention raises the inequality in payoffs among agents in networks with skewed degree distribution but reduces it for clustered topologies. The latter brings a novel explanation on why industries in the past have experienced a shift in the dominant pattern of knowledge exchange.

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As the famous quote says, ‘if you keep everything in-house, you will never generate as much’ (Alexander and Young 1996).

Under perfect IPR and collective invention regime, inequality rises even in clustered networks (compared to R&D alliances), and this is because only one out of the clique can make most valuable discoveries (first-mover advantage).

All capital letters have been replaced and all word containing digits, space or special characters together with the only two one-letter words were dropped resulting in the loss of about 30,000 words.

In the literature, one also finds correlation between patents’ number of citations with their technological importance and social value (Trajtenberg 1990; Albert et al. 1991). Alternatively, one can say that the more new inventions we can discover based on a certain patent, the higher its value (Fink et al. 2017).

In graph theory, clustering refers to the property that two nodes connected to a third node tend to also be connected between themselves.

This implies mutual interest in cooperation with subsequent flow of knowledge in both directions.

Allen (1983) described collective invention as a process in which knowledge was given away as a gift in the Cleveland steel industry to competitors within the local community of engineers.

In reality, of course, share in the joint payoff is subject to the contribution of each partner. However, to avoid complicated assumptions on how the payoffs shall be split, we always share them 50:50. Also, while in reality R&D alliances involving more than two partners take place, those alliances are exclusive and are not formed with all partners simultaneously. Allowing for only two partners per R&D alliance is a simple and convenient way of distinguishing alliances from collective invention.

See Appendix for technical details on how this sampling is implemented.

In particular, an exponential distribution is used. We tested also a normal distribution, and the results have no qualitative difference.

Presence of uncertainty allows agents to recognize a value behind an idea even when it contains no words from the accumulated knowledge stock of the agent.

Setting \(\delta \) too small results in a quick technological lock-in were agents see little possibility to recombine their accumulated knowledge stock, while setting it too large will presume agents foresee very complex technologies without learning enough about their building blocks. We set \(\delta =5\) in our model, but the findings are stable for small variation in this parameter.

If agents realize that the most valuable idea requires elements missing in their accumulated knowledge stock, they simply proceed with the second most valuable idea and so on.

While each agent takes evaluation of ideas by her partner into account at the time of cooperation, she disregards this evaluation afterward, when she, for instance, will consider whether to attempt that idea in a cooperation with a different partner.

It is worth noting that the more knowledge in common two agents have, the less productive is ceteris paribus their mutual effort in recombining new knowledge. In other words, given a fixed number of words and letters two agents have, the more knowledge they have in common, the less they can contribute to the joint pool of knowledge.

This is compatible with the so-called first to file patent rule, where the patent office grants the patent to those who file their application first.

Note that this results in a low network density which is in line with empirical literature (see Cowan and Jonard 2009 for a short review).

Sampling letters following the frequency those letters have in the vocabulary of words used (see Fig. 15 in Appendix) does not qualitatively change the results (similar number and value of words discovered, and the same ranking of scenarios with respect to their productivity and inequality; see Fig. 17) demonstrating robustness of our findings.

As at the very beginning agents have no words yet being generated. Also for the very first f periods, the agents can foresee the list of short words (of two and three letters) to see the value behind the ideas they attempt to realize.

We disregard the first 50 periods with respect to the number and value of words invented to omit the words discovered by purely random recombination.

Note that depending on the scenario in question, a single run of the model takes from 4 to 17 h using computer with four cores and 8 GB RAM. Therefore, we utilize the high-performance computing (HPC) cluster BwUniCluster https://wiki.bwhpc.de/e/Category:BwUniCluster_2.0.

Note again that while in R&D alliance an invention attempt is always an activity initiated by a pair of agents (an edge), in the collective invention regime it is a specific agent (node) that asks her social partners for help but appropriates all the benefits.

In Fig. 18 in Appendix, we show how the distribution of the Gini coefficient for the number of words invented evolves over time. At the very beginning, the inequality is largest because of few words invented by all agents. Within the next thirty to fifty periods the coefficient drops somewhat reaching its long term value and does not change much in subsequent periods.

The condition to be recorded was that the idea was novel for the receiving agent, and its value estimation by that agent was positive.

What is not shown in Fig. 12 but what is happening in reality for non-clustered networks is that when one of the agents gets an idea on what word to produce and shares this idea with her partners, those rarely find it valuable and do not pursue further.

Take an example the recombinant DNA technique recombining 24 distinct technology codes and now being the key technology in the biotechnology industry.

This is equivalent to the Erdös and Rényi (1959) algorithm of generating a random graph.

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Titel: On optimal regimes of knowledge exchange: a model of recombinant growth and firm networks
verfasst von: Ivan Savin
Publikationsdatum: 15.01.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Economic Interaction and Coordination / Ausgabe 3/2021
Print ISSN: 1860-711X
Elektronische ISSN: 1860-7128
DOI: https://doi.org/10.1007/s11403-020-00314-1

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