Knowledge Creation as a Square Dance on the Hilbert Cube

This paper presents a micro-model of knowledge creation and transfer in a small group of people. It is intended to contribute eventually to the development of microfoundations for aggregate models of knowledge externalities used in various literatures, such as those pertaining to endogenous growth theory, urban agglomeration and growth, organizational R&D and knowledge creation, and human capital accumulation. 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. In the two person case, we show that the equilibrium process tends to result in the accumulation of too much knowledge in common compared to the most productive state. Unlike the two-person case, in the four person case we show that under certain conditions, the equilibrium process of knowledge creation by four persons may converge to the most productive state. Extensions of the basic model are discussed.