Knowledge creation as a square dance on the Hilbert cube

Berliant, Marcus and Fujita, Masahisa (2007): Knowledge creation as a square dance on the Hilbert cube. Unpublished.

Abstract

This paper presents a micro-model of knowledge creation through the interactions among a group of people. Our model incorporates two key aspects of the cooperative process of knowledge creation: (i) heterogeneity of people in their state of knowledge is essential for successful cooperation in the joint creation of new ideas, while (ii) the very process of cooperative knowledge creation affects the heterogeneity of people through the accumulation of knowledge in common. The model features myopic agents in a pure externality model of interaction. Surprisingly, in the general case for a large set of initial conditions we find that the equilibrium process of knowledge creation converges to the most productive state, where the population splits into smaller groups of optimal size; close interaction takes place within each group only. This optimal size is larger as the heterogeneity of knowledge is more important in the knowledge production process. Equilibrium paths are found analytically, and they are a discontinuous function of initial heterogeneity.

• Item Type: MPRA Paper
• Institution: Washington University in St. Louis
• Language: English
• Keywords: knowledge creation; knowledge externalities; dynamic R and D; endogenous agent heterogeneity
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D83 - Search; Learning; Information and Knowledge; Communication; Belief; O - Economic Development, Technological Change, and Growth > O3 - Technological Change; Research and Development > O31 - Innovation and Invention: Processes and Incentives

References

Agrawal, A.K., Cockburn, I.M., McHale, J., 2003. Gone but not forgotten: Labor flows, knowledge spillovers, and enduring social capital. NBER Working Paper 9950 http://www.nber.org/papers/w9950 Aoki, M., 1994. The contingent governance of teams: Analysis of institutional complementarity. International Economic Review 35, 657-676. Barabási, A.-L., 2005. Network theory - the emergence of creative enterprise. Science 308, 639-641. Berliant, M., Fujita, M., 2006. Dynamics of knowledge creation and transfer: The two person case. http://econpapers.hhs.se/paper/wpawuwpga/0401004.htm Berliant, M., Reed, R., Wang, P., 2006. Knowledge exchange, matching, and agglomeration. Journal of Urban Economics 60, 69-95. Boldrin, M., Levine, D.K., 2005. Against Intellectual Monopoly. Mimeo. Duranton, G., Puga, D., 2001. Nursery cities: Urban diversity, process innovation, and the life cycle of products. American Economic Review 91, 1454-1477. Guimerà, R., Uzzi, B., Spiro, J., Amaral, L.A.N., 2005, Team assembly mechanisms determine collaboration network structure and team performance. Science 308, 697-702. Helsley, R.W. and W.C. Strange, 2004. Knowledge barter in cities. Journal of Urban Economics 56, 327-345. Hildenbrand, W., Kirman, A., 1976. Introduction to Equilibrium Analysis. North Holland/American Elsevier, Amsterdam. Holmstrom, B., 1982. Moral hazard in teams. The Bell Journal of Economics 13, 324-340. Jovanovic, B., Rob, R., 1989. The growth and diffusion of knowledge. The Review of Economic Studies 56, 569-582. Kaplinsky, R., 1983. Firm size and technological change in a dynamic context. The Journal of Industrial Economics 32, 39-59. Klein, E., Thompson, A.C., 1984. Theory of Correspondences. John Wiley & Sons, New York. Léonard, D., Van Long, N., 1992. Optimal Control Theory. Cambridge University Press, Cambridge. Scotchmer, S., 2004. Innovation and Incentives. MIT Press, Cambridge, MA.