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Cluster

by Lubrano Lavadera David Rosario (Submitted: 08/10/2007)

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WHAT IS IT?

The objective of this model is to study the dynamics of learning processes within industrial clusters, in relation to the structural properties of network relations. Industrial clusters are geographically localized production systems, characterized by a large number of small and medium sized firms that are involved at various phases of the production of a homogeneous product family. These firms are highly specialized in a few phases of the production process, and integrated through a complex network of interorganizational relationships (Becattini, 1990; Porter, 1998). Industrial clusters can be view as complex systems composed by many elements (firms) that interact among thems in a non-linear way. The system shows behaviors and patterns which emerge from the interactions among the system parts.

HOW IT WORKS

The agents represent the firms of the cluster. Every agent is in possession of a well defined a set of 3 competencies:
K = [c1 , c2 , c3]
where every dimension indicates the level of one competence. The level of knowledge is represented by a number in a scale from 0 to 100. Three types of agent are available, everyone of them is one expert on one competence.
Out of 90 agents, 30 agents (yellow color)are specialized in c1; 40 agents (green color) are specialized in c2; 20 firms (of blue color) are specialized in c3.
In addition every agent has its own absorptive capacity (AC). The AC is a construct used to measure a firm's ability to value, assimilate, and apply new knowledge (W. Cohen e D. Levinthal, 1990). The principal element to determine a firm’s absorptive capacity is represented by its available knowledge.
In the model to every agent AC a three dimensional vector is associated:
A-C = [a-c1, a-c2, a-c3]
where each dimension indicates the level of AC in one competence. The AC is a function of the knowledge level of the firms:
• a-c1 = c1 / 100
• a-c2 = c2 / 100
• a-c3 = c3 / 100
At the beginning of every simulation, any agent is supplied with a set competencies and the related AC. Later on, in the course of simulation, the set of competencies (and therefore the AC) is subject to continues changes, caused by two conflicting strength: learning and obsolescence.
There are two types of learning modes: internal and external. The internal learning is related to R&D activities and to the process of ”learning by doing” and “learning by using”. The external learning, instead, is related to process of “learning by interacting”, therefore firms can increase their knowledge trough continues inter-exchange within the relational network. The exchange of knowledge between two firms occurs only if they have complementary knowledge. Furthermore, the exchange is effective if the cognitive gap is not too high.
In addition to the set of competencies and to the absorptive capacity there is a third parameter which characterizes the agents: the number of interaction that any agent try to realize. This variable (that is signed in the model with the letter “ L”) is the same for every agent and it is established externally from the researcher. For example, if the L = 3, every agent, in any cycle, will continue to search a partner for cooperate until it doesn’t succeed to establish three relations.
If on one hand every firm keeps on learning during the simulation, on the other hand knowledge lose progressively value as it is subject to the obsolescence. This phenomenon competes to determinate the possibility of survival of the firm. If the firm doesn’t contrast knowledge decrease through a combination of the different ways of learning, it will risk to exit from the cluster. Therefore, in the model the obsolescence is a progressive decrease of knowledge levels . The decrease rate (indicated in the model as “obs”) affects in the same way every firm and it is established from the researcher, which can select a value between 0 and 1.

HOW TO USE IT

After choosing the number of firms to create, and setting the model variables, press the GO button.
Through model simulation it is to possible observe the formation of networks that evolve slowly until a stable configuration is reached. For different initial conditions, the cluster reacts spontaneously making a network of stable relations able to balance the two paired forces : learning and obsolescence.

THINGS TO NOTICE

For various values of obsolescence (0 ÷ 0,9) the cluster in any case tend to a high level of knowledge. Increasing the obsolescence the system seem to react by self – organizing exchanges and contrast the effect of obsolescence. This phenomenon can be interpreted as a consequence of the high flexibility of the system that allows firm to adapt efficiently to environmental changes. This ability of reacting to changes by reconfiguring the network of relationships is indeed one of the main properties of industrial clusters.
Usually the cluster forms a random network that, during the simulation, evolve toward a scale-free network, i.e. a networks with few leaders. So in the initial phase of the simulations the network is random type with a connective distribution that follows a bell curve. This means that, at the start of the simulation, every firms have more or less the same number of the connections. In the course of the simulation the network may evolve until it turns into a scale – free network that is characterized from a connective distribution which follow a power law. This mean that in the cluster there are few firms (firms -hub) whit a high number of links. To understand the mechanism that generates this phenomenon it was observed which nodes succeed at become hubs. The result was very interesting: the firms that, at the beginning, had a slightly greater number of connections were able to make a increasingly number of connections. Thus the model creates a mechanism similar to preferential attachment proposed by Barabasi. This result can be explained because in the cluster the firms with many links succeed to learn quickly and on all the 3 competences. This imply two outcomes:
1) the firm – hub is able to interacting with any type of the cluster firm
2) All the cluster firms wants to interact with the firms – hub because they have a elevated knowledge level (due to the high number of connections)
When the obsolescence value is 1 the firms do not succeed to learn enough to survive. Therefore in this condition all the cluster inevitably dies. The interesting thighs is that for obs = 0.9 the cluster still reaches a high average knowledge level. This threshold effects is the demonstration that the cluster is a non – linear system. When a non –linear system is in a critical condition little causes can generate devastating effect (in this case the death of all firms). This phenomenon can represent a point of weakness of the cluster which in given conditions may experience inability to innovate. To this end there is to say that the cluster firms are strongly interdependent among themselves. This causes on one hand high flexibility to market changes, but on the other hand, the network of relationships can represent an obstacle to best performing firms who are actually braked by the slower performances of other firms in the cluster.
The analysis shows that the system tends either toward high innovative potential or toward low innovative potential. No room is left for an intermediate behavior. This reflects another characteristics of real industrial clusters which can be easily classified in highly innovative or low innovative districts.

THINGS TO TRY

Change the number of the firms
Change obsolescence rate.
Change the number of links that each firm tries to create (L).
Change collaboration-probability. If you want to freeze the network in a given instant of the simulation, set the collaboration - probability value equal to 0.

EXTENDING THE MODEL

The model is a closed system since no new firms are allowed to enter the cluster. Try to include entrance of new firms and collaboration with external knowledge source (university, research center, etc..) that can influence the dynamics learning of the industrial cluster.

RELATED MODELS

See the models in the Networks section of the Models Library, such as Small World and Preferential Attachment.
The model was inspired from the article of Journal of Economic Dynamics & Control “Network structure and the diffusion of knowledge” , by Robin Cowan and Nicolas Jonard (2004). Here however the logic is reversed: Cowan and Jonard test the ability of several network structures to influence the learning performance. In this model instead it is the knowledge exchange that generate the network and its topological properties.

CREDITS AND REFERENCES

This model was development by Luca Iandoli and David Rosario Lubrano Lavadera at the University of Naples Federico II, Italy. This research activity has been carried out within CLOE, the Computational Laboratory of Organizational Engineering Research Group (www. coinor.unina.it/cloe) at the University of Naples Federico II

References
ALBINO V., CARBONARA N. and GIANNOCCARO I. (2003), Coordination mechanisms based on cooperation and competition within Industrial Districts: An agent-based computational approach, Journal of Artificial Societies and Social Simulation vol. 6, no. 4

AXELROD R. (2005), “Agent-based Modeling as a Bridge between Disciplines”, in Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics, Handbooks in Economics Series, North-Holland.

AXTELL R., EPSTEIN J. M. (1996), Growing Artificial Societies: Social Science from the Bottom Up, MIT Press, Cambridge, Mass.
BARABASI A., (2002), link, Einaudi.

BECATTINI G., 1990, the Marshiallian industrial district as socio - economic notion, , in Pyke, F., G. Becattini, W. Sengenberger (eds.), Industrial districts and inter-firm cooperation in Italy. International Institute for Labour Studies, Geneva, 37-51.

BOERO R., SQUAZZONI F. (2002), Economic Performance, Inter-Firm Relations and Local Institutional Engineering in a Computational Prototype of Industrial Districts, Journal of Artificial Societies and Social Simulation, vol. 5 (1).

BORRELLI F., PONSIGLIONE C., IANDOLI L. and ZOLLO G. (2005), Inter-Organizational Learning and Collective Memory in Small Firms Clusters: an Agent-Based Approach, Journal of Artificial Societies and Social Simulation vol. 8, no. 3

BRUSCO S., MINERVA T., POLI I e SOLINAS G. (2001), Un automa cellulare per lo studio del distretto industriale, Università degli Studi di Modena e Reggio Emilia, Dipartimento di Economia Politica

COHEN W., LEVINTHAL D. (1989), Innovation and Learning: The Two Faces of R&D, Economic Journal, vol. 99 (397), pp. 569-596.
COWAN R., JONARD N., (2004), Network structure and the diffusion of knowledge Journal of Economic Dynamics & Control.

EPSTEIN J. M., 2005, “Remarks on the foundations of agent-based generative social science”, in Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics, Handbooks in Economics Series, North-Holland.

FIORETTI G. (2001), Information structure and behavior of a textile industrial district, Journal of Artificial Societies and Social Simulation. vol. 4, no. 4.

FIORETTI G., 2005, "Agent-Based Models of Industrial Clusters and Districts", Contemporary Issues in Urban and Regional Economics, Frank Columbus ed., Nova Science Publishers.

HOLLAND H. (1998), Emergence from chaos to order, Oxford University Press, Oxford.
PORTER M., 1998, Clusters and the new economics of competition Harvard Business Review; Boston.

TERNA P., BOERO R., MORINI M., SONNESSA M. (2006), Modelli per la complessità - La
simulazione ad agenti in economia, Ed. Il Mulino, Bologna.

TESFATSION L., 2005, “Agent-Based Computational Economics: A Constructive Approach to Economic Theory”, in: Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics, Handbooks in Economics Series, North-Holland.

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