Small worlds and the dynamics of networks

This work focuses both on the relationship between network architectures and network performance, and on the dynamics of network creation and evolution. In particular, we use the network structure to model the way a population of agents creates and diffuses knowledge. Because so much important knowledge remains tacit, and thus transmits effectively only over short distances, the network structure underlying communication among different agents becomes central to the way an economy will create, use and diffuse knowledge. A central question in this research is whether there are identifiable network structures that perform better in terms of knowledge creation and diffusion, than do others. Small world networks have been found efficient and common in other fields, and one aspect of this research is to ask whether the effectiveness of small worlds carries over into the economics of knowledge. Network creation and evolution are driven by pairs of agents forming and breaking bilateral links. Again in the context of knowlege creation, the point of link creation is to access complementary knowledge. This takes place in different social, informational and innovation contexts. Part of the goal of our work here is to understand how these context affect the types of networks that emerge at the aggregate level, and how an agent's position in the emergent network affects his or her performance.

Some Papers

Cowan, Robin and Nicolas Jonard, "Interactions between the formal and the informal: Network structures and organizational performance",

Abstract Although the literature recognizes that informal and formal elements are central in driving individual and thus organizational behaviour and performance, the joint and reciprocal effects of formal and informal have been under-explored. In this respect, the present paper makes three contributions. First, it presents a simple, general, computational model that permits examination of the interactions between different formal and informal structures, and how those interactions affect organization performance. Second, the paper uses psychology results to model how informal and formal, intra-firm structures jointly determine agents' productivity levels, and reveals how changes in quality and quantity of social interaction alter both mean and variance of firm performance. Third, the paper introduces the idea that there may be important contingencies affecting the relationship between alignment and performance, and it demonstrates the moderating role of organizational modularity which can mitigate or exacerbate the effects of formal and informal interactions.

Baum, Joel, Robin Cowan and Nicolas Jonard, "Network-independent partner selection and the evolution of innovation networks", Management Science. 56: 2094-2110, 2010. doi10.1287/ mnsc.1100.1229

Abstract Empirical research on strategic alliances has focused on the idea that partners are selected on the basis of social capital considerations. In this paper we emphasize instead the role of complementary knowledge stocks and knowledge dynamics, which have received surprisingly limited attention relative to social capital as forces behind the formation and dynamics of innovation networks. To marshal evidence in this regard, we design a simple model of partner selection in which firms ally for the purpose of learning and innovating, and in doing so create an industry network. We abstract completely from network-based structural and strategic motives for partner selection and focus instead on the idea that firms' knowledge bases must "fit" in order for joint leaning and innovation to be possible, and thus for an alliance to be feasible. The striking result is that despite containing no social capital considerations, this simple model replicates the firm conduct, network structure, and contingent effects of network position on performance observed and discussed in the empirical literature.

Cowan, Robin and Nicolas Jonard, " If the Alliance Fits ... : Innovation and Network Dynamics" in J.A.C. Baum and T.J. Rowley (eds.) Network Strategy: Advances in Strategic Management, 25. Oxford UK: JAI/Elsevier, 2008. Also available as UNU-MERIT Working Paper # WP2008-022 ,

Abstract Network formation is often said to be driven by social capital considerations. A typical pattern observed in the empirical data on strategic alliances is that of small world networks: dense subgroups of firms interconnected by (few) clique-spanning ties. The typical argument is that there is social capital value both to being embedded in a dense cluster, and to bridging disconnected clusters. In this paper we develop and analyze a simple model of joint innovation where we are able to reproduce these features, based solely on the assumption that successful partnering demands some intermediate amount of similarity between the partners.

Cowan, Robin and Nicolas Jonard, " Knowledge Portfolios and the Organization of Innovation Networks" Academy of Management Review vol 34, pp. 320-342, 2009.

Abstract Properties of strategic alliance networks such as small worlds, skewed link distributions and patterns of repeated tie occurrences are often explained in terms of social capital theories. A simple model shows that merely assuming that firms must have a certain degree of commonality in their knowledge to have a successful alliance, is enough to produce the above features, without recourse to social capital at all.

Cowan, Robin and Nicolas Jonard, " Structural Holes, Innovation and the Distribution of Ideas", vol (2), pp 93-101, Journal of Economics of Interaction and Co-ordination, DOI: 10.1007/s11403-007-0024-0, 2007.

Abstract We model knowledge diffusion in a population of agents situated on a network, interacting only over direct ties. Some agents are by nature traders, others are by nature "givers": traders demand a quid pro quo for information transfer; givers do not. We are interested in efficiency of diffusion and explore the interplay between the structure of the population (proportion of traders), the network structure (clustering, path length and degree distribution), and the scarcity of knowledge. We find that at the global level, trading (as opposed to giving) reduces efficiency. At the individual level, highly connected agents do well when knowledge is scarce, agents in clustered neighbourhoods do well when it is abundant. The latter finding is connected to the debate on structural holes and social capital.

Robin Cowan, "Network models of innovation and knowledge diffusion" in Clusters, Networks and Innovation, S. Breschi and F. Malerba (eds.) Oxford University Press: Oxford, pp. 29-53, 2005. Also available as: MERIT Research Memorandum # RM2004-016, (RM2004-016)

This is a paper that surveys some of the recent developments in networks and industrial dynamics.

Robin Cowan, Nicolas Jonard and Jean-Benoit Zimmermann, "Bilateral Collaboration and the Emergence of Networks" Management Science, vol 53(7), pp. 1051-1067, 2007. An earlier version circulates as: " Networks as Emergent Structures from Bilateral Collaboration ", MERIT Research Memorandum # RM2004-017.

Abstract In this paper we model the formation of innovation networks as they emerge from bilateral actions. The effectiveness of a bilateral collaboration is determined by cognitive, relational and structural embeddedness. Innovation results from the recombination of knowledge held by the partners to the collaboration, and the extent to which agents' knowledge complement each others is an issue of cognitive embeddedness. Previous collaborations (relational embeddedness) increase the probability of a successful collaboration; as does information gained from common third parties (structural embeddedness). As a result of repeated alliance formation, a network emerges whose properties are studied, together with those of the process of knowledge creation. Two features are central to the innovation process: how agents pool their knowledge resources; and how agents derive information about potential partners. We focus on the interplay between these two dimensions, and find that they both matter. The networks that emerge are not random, but in certain parts of the parameter space have properties of small worlds.

Robin Cowan, Nicolas Jonard and Jean-Benoit Zimmermann, "Evolving Networks of Inventors"Journal of Evolutionary Economics 16, pp. 155-174, 2006.

Abstract In this paper a model for the formation of strategic alliances is studied. Innovation results from the recombination of knowledge held by the partners to the collaboration, and from the history of their collaboration. Innovation brings partners closer together, while at the same time the repetition of partnerships fosters trust and helps improving the outcome of each round of cooperation. A tension exists between innovating with people I know in order to reduce uncertainty at the expense of the net benefit from our joint effort, and innovating with strangers with whom the outcome of joint innovation can be greater but at a larger risk of failure. This ``organized proximity'', built through the experience of cooperation, can be at the origin of strongly structured networks of innovation, where agents' relations focus on limited cliques of partners.

Robin Cowan and Nicolas Jonard, "Information Technology and the Dynamics of Joint Innovation" MERIT Research Memorandum #2004-014

Abstract We develop a model of an innovative industry to examine how information technology, by both enhancing matching efficiency and knowledge sharing, can have an ambiguous effect on the total amount of innovation. We consider a population of firms holding different knowledge expertise, and forming partnerships to conduct joint R\&D. We assume that bringing together different expertise has positive value for innovating but also that joint innovation implies a partial convergence of the partners' expertise. We study how the distribution of firms changes and thus how the innovative potential of the economy evolves. We show that as heterogeneity is used as an input by the innovative process, the industry must eventually collapse to a unique expertise, but how fast this takes place depends on the quality of IT. As a result of falling dispersion, a tension arises between static and dynamic efficiency.

Robin Cowan and Nicolas Jonard, Network Structure and the Diffusion of Knowledge Journal of Economic Dynamics and Control, 28/8 pp. 1557-1575, 2004.

Abstract This paper models knowledge diffusion as a barter process in which agents trade different types of knowledge. It captures the observed practice of informal knowledge exchange among agents with related, though different knowledge. Agents are located on a network and are directly connected with a small number of other agents. They repeatedly meet those with whom direct connections exist and trade if mutually profitable trades exist. In this way knowledge diffuses throughout the economy. We examine the relationship between network structure and diffusion performance. At one extreme every agent is connected to n nearest neighbours. At the other extreme every agent is connected to, on average, n agents located at random in the network, and we examine the space of structures that fall between these extremes. We find that the performance of the system exhibits clear "small world" properties, in that the steady state level of average knowledge is maximal when the structure is that of a small world (that is, when most connections are local, but roughly 10 percent of the connections are long distance). It is also the case that the variance of knowledge levels among agents is maximal in the small world region. We explain both these results as reflecting the dynamics of knowledge transmission as affected by the nature of connections among agents.

Robin Cowan and Nicolas Jonard "The Dynamics of Collective Invention" Journal of Economic Behavior and Organization, vol 52(4) pp. 513-532, 2003. .

Abstract This paper models the phenomenon of collective invention. Collective invention exists when the disclosure of information among competing entities creates a positive feedback that allows for high innovation rates and fast knowledge accumulation. Conditions for collective invention exist today in institutions such as the virtual communities (LINUX, or open source software groups e.g.) enabled by the Internet. We develop a formal model that accounts for the dynamics of knowledge and collective invention, and examine how the architecture of the network of agents influences patterns and rate of innovation. We find that the communication network structure has a strong influence on system performance. The small world structure stands out as an efficient architecture for knowledge growth when absorption capacities are low. Large absorbing capacities, by contrast, emphasize the performance of random worlds, i.e., the value of short path length. Small worlds also generate a relatively equal distribution of knowledge over agents. Spatial correlation in knowledge levels exists and is affected by network architecture, but does not display small world properties however.

Robin Cowan and Nicolas Jonard, "Knowledge Creation, Knowledge Diffusion and Network Structure"

Abstract This paper models knowledge creation and diffusion as processes involving many agents located on a network. Knowledge diffusion takes place when an agent broadcasts his knowlsedge to the agents to whom he is directly connected. Knowledge creation arises when agents receive new knowledge which is combined with their existing knowledge stocks. Thus both creation and diffusion are network-dependent activities. This paper examines the relationship between network architecture and aggregate knowledge levels. We find that knowledge growth is fastest in a "small world", that is, when the underlying network structure is relatively cliquish (dense at the local level) yet has short paths. this corresponds to a locally connected graph which includes a few long-distance connections or shortcuts.

Robin Cowan, Nicolas Jonard and Muge Ozman, "Knowledge Dynamics a Network Industry" Technological Forecasting and Social Change, 71(5), pp. 469-484 2004.

Abstract In this paper, we model the impact of networks on knowledge growth in an innovating industry. Specifically, we compare two mediums of knowledge exchange; random interaction, and the case in which interaction occurs on a fixed architecture. We investigate how the medium of knowledge exchange contributes to knowledge growth under different scenarios related to the industry's innovative potential. We measure innovative potential by considering the extent to which knowledge can be codified, and the available technological opportunities. Our results tend to support the conjecture that spatial clustering generates higher long run knowledge growth rates in industries characterized by highly tacit knowledge, while the opposite is true when the degree of codification is important.

Robin Cowan, Nicolas Jonard and Jean-Benoit Zimmermann, "On the Creation of Networks and Knowledge" in The Complex Dynamics of Economic Interaction, M. Gallegati, A. Kirman and M. Marsili, (eds.), Springer, 2004. 2004.

Abstract This paper examines the evolution of networks when innovation takes place as a result of agents bringing together their knowledge endowments. Agents freely form pairs creating a globally stable matching. paired agents combine their existing knowledge to create new knowledge. We study the properties of the dynamic network formed by these interactions, and the resultant knowledge dynamics. Each agent carries an amount of knowledge of a certain type, and the innovative output of a pair is a function of the partners' endowments and types. We find evidence that the pattern of substitution between quantity and type of knowledge in the innovation function is vital in determining the growth of knowledge, the emergence of expertise and the stability of a number of network structures. Network structure itself exhibits a phase change when the relative importance of diversity compared to quantity increases beyond a threshold value.


Nicolas Jonard, CNRS, and University of Luxembourg

nicolas.jonard at

Joel Baum, Rotman School of Management, University of Toronto

jbaum at

Muge Ozman, MERIT, Universiteit Maastricht; Maastricht, Netherlands.

m.ozman at

Jean-Benoit Zimmermann, CNRA, GREQAM; Marseille, France.

jbenoit at

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