  We develop a new framework for modeling innovation networks which evolve over
time. The nodes in the network represent firms, whereas the directed links
represent unilateral interactions between the firms. Both nodes and links
evolve according to their own dynamics and on different time scales. The model
assumes that firms produce knowledge based on the knowledge exchange with other
firms, which involves both costs and benefits for the participating firms. In
order to increase their knowledge production, firms follow different strategies
to create and/or to delete links with other firms. Dependent on the information
firms take into account for their decision, we find the emergence of different
network structures. We analyze the conditions for the existence of these
structures within a mathematical approach and underpin our findings by
extensive computer simulations which show the evolution of the networks and
their equilibrium state. In the discussion of the results, particular attention
is given to the emergence of direct and indirect reciprocity in knowledge
exchange, which refers to the emergence of cycles in the network structure. In
order to motivate our modeling framework, in the first part of the chapter we
give a broad overview of existing literature from economics and physics. This
shows that our framework bridges and extends two different lines of research,
namely the study of equilibrium networks with simple topologies and the dynamic
approach of hypercycle models.

Physics and Society