Abstract
The aim of this paper is to extend the theoretical literature on knowledge and network structure by studying the use of social networks as a learning mechanism. The novelty of this approach is suggested by the empirical evidence on informal trading of know-how. In the model, we consider a set of actors who create and diffuse knowledge with the aim of increasing their own personal knowledge. They are located on a lattice (identifying the social space) and are directly connected to a small number of other individuals. We assume that individuals can learn individually or socially, and that individuals choose how to learn on the basis of a cost-benefit comparison. Within this framework, we compare network structures in terms of efficiency and equity. We find that the opportunity cost of using the network affects its optimal structure in terms of aggregate performance and that the small world does not emerge unambiguously as being the most efficient.
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Notes
“Given that the amount of time and energy that a given individual has available for trading is limited each is likely to try to maximize the useful yield of his trading” (Carter 1989, p. 157).
The discussion on cliques, structural holes and small worlds can be related to the concept of strong and weak ties (Granovetter 1973), where the strength of a tie depends on a combination of time, emotional intensity, intimacy and reciprocal service. Granovetter’s argument is based on the following assumption: if an individual (say A) has strong ties with other two persons (say B and C), then it is not possible for the tie between B and C to be absent. This assumption, based on some empirical results, has a logical implication: only weak ties can bridge two subsets of the network. “If each person’s close friends know one another, they form a closely knit clique. Individuals are then connected to other cliques through their weak rather than their strong ties. Thus, from an aerial view of social networks, if cliques are connected to one another, it is mainly by weak ties.” (Granovetter 2005, p. 34). Therefore it seems plausible to consider links inside cliques to be strong ties, and links outside cliques (bridging structural holes) as weak ties.
The empirical literature on informal know-how trading often claims that individuals ask for help when they have to solve some technical or practical problem (e.g. which material is better to use). Our representation of a learning episode as the increase of an argument of vector V i (t) can be interpreted as the accumulation of a piece of knowledge that could be useful for the solution of a problem.
In the long run, it is reasonable to assume that decreasing returns in learning prevail, so that the rate at which knowledge is accumulated through individual learning decreases. However, since we intend to model a situation of rapid technological or scientific change, we ignore this issue.
Suppose, for instance, that there are five knowledge categories, α = 0.5 and \( \overline{\beta } = 0.02 \). For agent i, \( V_{{i,1}} {\left( t \right)} = 10 \) and \( V_{{i,k}} {\left( t \right)} = 8 \) for all the other k. For agent j, \( V_{{i,k}} {\left( t \right)} = 8 \) for all k. Total gain from bartering is 1; expected total gain from individual learning is 0.18. In this case, bartering does not occur, even if it is socially desirable. Side-payments are not allowed in this model. Consistent with the empirical evidence, we assume that the agent who gains more from the barter cannot compensate through monetary transfer the agent who gains less.
For instance, Giuliani and Bell (2005) show that firms with more absorptive capacity have more external links. In their paper, absorptive capacity is proxied by education and experience of technical personnel and firms’ R&D intensity. Then, their result can also be interpreted in terms of firms’ capability to provide useful knowledge to their partners.
This parameterization is the same as that adopted in Cowan and Jonard (2004).
In terms of interpreting the time horizon, we note the following. Since each agent has a probability 1/250 to be drawn each period, in expected value every agent will have an opportunity to learn every 250 periods. Then, it is plausible to define this as the basic unit of time. If the empirical counterpart of this basic unit is one week, the time horizon considered will correspond to approximately 8 years.
We ran other numerical experiments, but without any other economic insights than those reported in this paragraph. We also computed confidence intervals for the statistics reported in the paper, but since these turned out to be very small, we omit them from the graph for the sake of readability.
This can be seen in the graphs for the non normalized Herfindhal index, not reported here.
Figure 5 shows that. for high \( \overline{\beta } \), the coefficient of variation of small world increases compared to the coefficient of variation for the regular network; the trade off then presumably will vanish. What we maintain, however, is that, for a significant period of time, such a trade-off exists.
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A previous version of this paper has circulated under the title “Social networks as option and the creation and diffusion of knowledge”. We thank participants in the I-NECK meeting, May 2004, Pompeu Fabra University, Barcelona, the Druid PhD conference, January 2004, Aalborg, and a seminar at GREQAM, Marseille, November, 2005, for useful comments and suggestions. Moreover, we are indebted to two anonymous referees for valuable comments. The usual disclaimers apply.
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Cassi, L., Zirulia, L. The opportunity cost of social relations: On the effectiveness of small worlds. J Evol Econ 18, 77–101 (2008). https://doi.org/10.1007/s00191-007-0073-5
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DOI: https://doi.org/10.1007/s00191-007-0073-5