Abstract
In this work we analyze the evolving dynamics of different strategies of collaborative networks that emerge from the creation and diffusion of knowledge. An evolutionary economic approach is adopted by introducing decision rules that are applied routinely and an agent-based model is developed. Firms (the agents) can collaborate and create networks for research and development purposes. We have compared three collaboration strategies (A—peer-to-peer complementariness, B—concentration process and C—virtual cooperation networks) that were defined on the basis of literature and on empirical evidence. Strategies are introduced exogenously in the simulation. The aims of this paper are twofold: (i) to analyze the importance of the networking effects; and (ii) to test the differences among collaboration strategies. It was possible to conclude that profit is associated with higher stock of knowledge and with smaller network diameter. In addition, concentration strategies are more profitable and more efficient in transmitting knowledge through the network. These processes reinforce the stock of knowledge and the profit of the firms located in the centers of the networks.
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Notes
According to Axelrod and Benett (1997), emergence is a consequence of local interaction of agents: the large-effects of complex locally interacting individuals endorse the appearance of emergent properties at the level of the population.
For the sake of simplification the index t is not considered in some expressions for which the time is not important in the analysis.
Several topologies are described in literature about collaboration networks, being these the most common topologies of the emerging networks. For a more detailed description of topologies, see Wilhite (2006).
MC change with the market. First we computed a marginal cost for each type of market according to a Normal distribution, as follows: market \({\mathrm{X}}: {\mathrm{MC}}_\mathrm{X}\sim {\mathrm{N}}(0.1, 0.01); {\mathrm{market}}\, {\mathrm{Y}}_{1}: {\mathrm{MC}}_\mathrm{Y1}\sim {\mathrm{N}}(0.05, 0.005); {\mathrm{market}} {\mathrm{Y}}_{2}: {\mathrm{MC}}_\mathrm{Y2}\sim {\mathrm{N}}(0.05, 0.005)\).
According to Scitovsky (1954), spillovers (or technological externalities) deal with the effects of non-market interactions, being realized through processes that affect the production (or profit) function of a firm. Spillovers may respect to the diffusion of learning across firms, which can take place through interfirm mobility of employees or cooperation.
Without loss of generality, we assume that \({\mathrm{D}}_\mathrm{tech} = 0.75\) and \({\mathrm{D}}_\mathrm{geo} = 0.25\), giving more importance to the technological distance than to the geographical one, which seems to be in line with empirical evidence.
Although the mechanisms underlying innovation are often unknown, we consider the use of the Normal distribution for updating \({\mathrm{w}}_\mathrm{i}^\mathrm{t}\) because there are many small and independent effects in the stock of knowledge that additively contribute to each observation. This model is in line with the work of Carayol and Roux (2005), in which networking allows the flow of R&D innovation to spread within a network and, consequently, to increase the stock of knowledge of other firms that are connected in the same network, as a function of the distance between nodes.
For instance, a final good producer (e.g. car makers) detains a specific stock of knowledge in its industry but may also hold some knowledge about intermediate goods industries (e.g. carburetors or clutches suppliers). Additionally, this complementarity may be incorporated in the definition of collaboration strategies (Sect. 3.4).
Following these stages, networks are created from the bottom up, according to individual decisions taken by firms. The aggregate behaviour (at network level) is produced by the interaction of individual agents. According to Axelrod and Benett (1997), these networks are defined as emergent in the scope of the multi-agent system.
If more than one firm satisfies the given condition, then one is chosen at random among the firms that are in the same conditions.
R is a language and environment for statistical computing and graphics (R Development Core Team 2010)
The Mann–Whitney test of independence presented the following \(p\) values: Profit \((<0.1\,\%)\), marginal cost (4 %), stock of knowledge (0.1 %). The Mann–Whitney test (Conover 1999), also known as the Mann–Whitney non parametric U test involves studying the position or ranking of data of two independent samples (defined by 1 and 2—in our case the two independent samples correspond to the grouping firms in networks and firms not in networks).
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Campos, P., Brazdil, P. & Mota, I. Comparing Strategies of Collaborative Networks for R&D: An Agent-Based Study. Comput Econ 42, 1–22 (2013). https://doi.org/10.1007/s10614-013-9376-9
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DOI: https://doi.org/10.1007/s10614-013-9376-9