https://orcid.org/0000-0002-5596-0151
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ABSTRACT
Interventions targeting the support of interregional knowledge networks have become an increasingly important part of modern regional development policy. However, our knowledge is limited with respect to the potential economic effects of concrete policy interventions. In order to examine these effects, we developed an agent-based model of network formation. We discuss the model in detail and provide the results of a simulation that illustrates how the agent-based model might be applied to help solve an important practical problem, namely prioritization, in Smart Specialisation policy.
ACKNOWLEDGEMENTS
The authors thank Anna Csajkás for professional research assistance and Orsolya Hau-Horváth for a contribution to a former version of the model presented in this paper. The authors also thank Manfred Paier and Thomas Scherngell for useful comments.
DISCLOSURE STATEMENT
No potential conflict of interest was reported by the authors.
ORCID
Tamás Sebestyén http://orcid.org/0000-0002-5596-0151
Attila Varga http://orcid.org/0000-0001-7252-5648
Notes
1. The shortest path between nodes A and B is the minimum number of links through which B can be reached from A. If the links are weighted, representing connection intensities or proximities, then the inverse of these weights are used to calculate shortest paths. See, for example, Wasserman and Faust (Citation1994) or Barabási (Citation2016) for more details.
2. The choice of the two-dimensional Euclidean space is driven by necessity: by increasing the dimensionality, the mapping and the fitting procedures require an exponentially increasing computational time, making simulations like the one shown in this paper impossible. Also, this low-dimensional representation enables a graphical representation of agents’ motion, which contributes to the interpretation of the results. On the other hand, this reduction in dimensionality limits the capabilities of the model: the fewer dimensions used, the more likely it is that agents unintentionally cross the path of other agents that they do not find attractive initially. Although this effect may be realistic on a small scale (unintended but useful encounters), it distorts the results when overrepresented.
3. As mentioned above, different types of proximities may be applied. In our model, we use cognitive and social proximities in the model.
4. For some stylized models of network formation with a cost factor, see, for example, Bala and Goyal (Citation2000), Jackson and Wolinsky (Citation1996) or Carayol and Roux (Citation2009).
5. See the third section for the details on the estimated gravity equation.
6. If there are N agents in the model, parameter AP takes integer values between 1 and and shows the number of other agents one can keep pace of. We assume that agents only take into account the first AP most attractive partners. If
, then they have full information, whereas if
, then they only ‘follow’ the most attractive agent.
7. See Appendix A in the supplemental data online for details of the implementation of speed heterogeneity.
8. See Appendix A in the supplemental data online for details of the implementation of counterforce heterogeneity.
9. See the third section for details on the specification of the gravity model.
10. The simulation exercise described here illuminates the possible uses of the model. The general model set-up is ready to install agents at the institutional level given that data are available.
11. For networks of co-publication, see, for example, Abbasi, Altmann, and Hossain (Citation2011), Abbasi, Hossain, and Leydesdorff (Citation2012), Hopp, Iravani, Liu, and Stringer (Citation2010) or Rumsey-Wairepo (Citation2006). Co-patenting networks are examined by Maggioni et al. (Citation2011) or Cassi and Plunket (Citation2015), among others.
12. In these programmes, institutions and firms from different regions engage in cooperative research projects of different lengths and the collaborative nature of these projects allows one to infer on cooperation intensities between regions.
13. These large changes are most likely in the case of less central regions – the majority – where one big project may significantly influence the cooperation intensities from one year to the other in the starting and ending years of the project.
14. See Appendix B in the supplemental data online for details on this.
15. Although cooperation intensities and social distances are based on the same information, they reflect different things. While cooperation intensities show direct connections between agents, social distance refers to network distances, on the one hand, which take into account indirect partners and ties and, on the other, it is based on two-dimensional distances achieved through MDS which adds a technical wedge between cooperation intensities and social distance.
16. The reference period against which these time dummies are defined is the first year of the sample.
17. For the range of the parameters on which the optimal parameter setting is searched, see Appendix G in the supplemental data online.
18. Convergence is assumed when the percentage change in the mean pairwise social distance (from the start of the simulation to the current period) remains below ±0.01%. As agents may ‘fluctuate’ around their steady-state position, we run the model for 50 periods after achieving convergence, and the final equilibrium positions and attraction values after the shock are calculated as the average over these 50 overrun periods.
19. Appendix C in the supplemental data online provides more information about the genetic algorithm used.
20. Setting the counterforce parameter below unity does not eliminate the stationary nature of the model. Only agents need more time to arrive into a new steady state and move farther from their initial positions.
21. Large observation means higher than average collaboration intensity over the whole sample. The average collaboration intensity is 2.45, which means roughly 2.5 joint projects between regions.
22. Appendix D in the supplemental data online provides the technicalities behind the motion of agents in the social space.
23. The ENQ index thus captures not only direct connections of an actor but also its embeddedness in the entire network.