Saint-Etienne, France. âNETWORKS of INNOVATION and SPATIAL ANALYSIS of KNOWLEDGE DIFFUSIONâ. Micro economic agent model of innovation ...
ADRES International Conference 2006, September, 14th and 15th. Saint-Etienne, France “NETWORKS of INNOVATION and SPATIAL ANALYSIS of KNOWLEDGE DIFFUSION”
Micro economic agent model of innovation networks By M. König, F. Schweitzer and S. Battiston ETH Zurich, Switzerland
Abstract Our paper presents a microeconomic model of heterogeneous agents interacting in a network, which catalyzes the agent's output by means of innovations. Innovation processes involve the transfer of knowledge from one agent to another. These agents could be companies research labs etc. and their interaction can be described in the form of a network, where different agents are represented as nodes and their interaction by unidirectional links. Unidirectional means that one agent may boost the production of another but the reverse is not mandatory. Moreover, in many cases the resources provided by an agent are not depleted because of the interaction with other agents. This holds in particular for the transfer of knowledge, because there is no conservation law, so an agent can share it with others without facing a loss of knowledge. As Jones [1] states, ''Ideas are different from nearly all other economic goods in that they are nonrivalrous''. Saxenian [2] has shown that geographic proximity is not a sufficient prerequisite for the creation of networks of interacting agents. Moreover, the building up of knowledge in a network of economic agents is not necessarily subject to geographical constraints. Modern means of transport and communication devices have created new possibilities of knowledge exchange and interaction. On the other hand a notion of proximity in terms of degrees of separation on a network of interactions plays also an important role. In our model we therefore do not concentrate on geographical proximity but rather on a network of relations. We consider competition as one of the main driving factors in knowledge and innovation networks. ''The threat of entry by an outsider pushes forward the innovative effort. Competition in the race to innovate stimulates innovation'' [3]. We study a model of knowledge exchange in which selfish agents build up a network of interactions. The agents knowledge levels can only be increased through interaction. We assume that the knowledge level of an agent, which is not interacting at all with other agents, vanishes after a certain time. In addition each connection of agents results in costs that can be interpreted as the time an agent must spend with another in order to maintain the link (opportunity costs). The agent's utility is then composed of the benefits as well as the costs through interaction. We assume a minimum level of intelligence of agents which leads to two reasonable rules governing the evolution of the links in the network between agents [4,5]. First, randomly chosen agents can create bilateral connections. This means that two links are created between unconnected agents and in the case of an already existing link a second link is added. This bilateral connection is then accepted only if both agents strictly benefit from it. Secondly we consider the unilateral deletion of links. One outgoing link of a randomly selected agent is deleted if this increases the utility of that agent. Providing the agents with a higher level of intelligence we modify the rules for creating and deleting links. We assume that an agent can preferably form mutual connections with neighbors of its neighbors. This means it can try by which it profits most. Again this creation of a mutual connection has to strictly improve the knowledge levels of both agents involved. In this more realistic setting an agent tests all its neighbors separately and removes the connection to that agent, which contributes to his payoff the least.
ADRES International Conference 2006, September, 14th and 15th. Saint-Etienne, France “NETWORKS of INNOVATION and SPATIAL ANALYSIS of KNOWLEDGE DIFFUSION”
In the paper, we discuss various results for the network evolution. We investigate the impact of different parameter setsdetermining the costs and benefits of the knowledge growth function. Trivial results of equilibrium networks are an empty graph which contains only isolated vertices and on the other hand a complete graph containing all possible links. Random graphs [6,7] lie in between these two types of networks. We will use random graphs as a reference case and will compare the equilibrium networks resulting from our simulations to this. We discuss different mechanisms stipulating the creation and deletion of links and show their influence on the possible equilibrium outcomes of the network configuration. When agents update their links with a minimum level of knowledge, as described above, and the costs are sufficiently low then the network evolves from an empty graph to a homogeneous network. This network shows similar distributions of node degrees as random graphs and a Poisson like distribution of knowledge levels. If the costs are sufficiently increased, then the network decomposes into pairwise connected agents. This is reflected in the number of disconnected components and an average degree of one. Assuming a higher level of intelligence the system becomes more heterogeneous and shows assortativity [7] of node degrees and correlations of knowledge levels. We identify the conditions which correspond to the emergence of cycles of cooperating agents. We compare the distribution of cycles in our model with the distribution of cycles in random graphs [8,9]. We further identify those parameter settings and mechanisms which make the emergence of non-random cooperative structures possible. We investigate average, variance of knowledge levels and skewness of the knowledge distribution as well as knowledge correlations. In this context we discuss different measures of system performance and the antipode of equality vs. inequality of knowledge allocation [10]. References [1] Charles I. Jones. Growth and ideas. NBER Working Papers 10767, Department of Economics, U.C. Berkeley and National Bureau of Economic Research (NBER), September 2004. URL http://ideas.repec.org/p/nbr/nberwo/10767.html. [2] A. Saxenian. Regional Advantage: Culture and Competition in Silicon Valley and Route 128. Harvard University Press, Cambridge, 1994. [3] Zvi Griliches and T. Jakob Klette. Empirical patterns of firm growth and R&D investment: A quality ladder model interpretation. The Economic Journal, 110:363–387, April 2000. [4] Matthew O. Jackson. A survey of models of network formation: Stability and effciency. Working Papers 1161, California Institute of Technology, Division of the Humanities and Social Sciences, 2003. URL http://ideas.repec.org/p/clt/sswopa/1161.html . [5] Matthew O. Jackson and Alison Watts. The evolution of social and economic networks. Journal of Economic Theory, 106(2):265–295, 2002. URL http://ideas.repec.org/a/eee/jetheo/v106y2002i2p265295.html . [6] B. West, Douglas. Introduction to Graph Theory. Prentice-Hall, 2nd edition, 2001. [7] M.E.J. Newman. The structure and function of complex networks. SIAM review, 45(2):167–256, 2003. [8] Bela Bollobas. Modern Graph Theory. Graduate Texts in Mathematics. Springer, 1998. [9] Bela Bollobas. Random Graphs. Cambridge University Press, 2nd edition, 1985. [10] Robin Cowan and Jonard Nicolas. Network structure and diffusion of knowledge. Journal of Economic Dynamics and Control, 28:1557–1575, 2003.
