The Evolution of Firm Connections in Networks: A Differential Game Approach

Abstract

Optimal control theory can be employed to gain novel insights on the self-organization and structure of networks. We develop a Cournot differential game to analyse the evolutionary dynamics of firm connections within a network. We determine the feedback (Markovian) Nash equilibrium strategies and the steady state of the model and identify the key factors affecting the strategic choice of network firms. Our model confirms the empirical evidence that network firms tend to increase their own connections over time; moreover, such growing connections are mainly affected by the market size and the spillover rate.