Transition Dynamics in a Network Game with Heterogeneous Agents: the Stochastic Case

Stochastic parameters are introduced into a model of network games with production and knowledge externalities. The model was formulated by V. Matveenko and A. Korolev and generalizes Romer’s two-period model. The agents’ productivities have both deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle that occurs in the process of combining the agents. Explicit expressions for the dynamics of a single agent and dyad agents are obtained in the form of Brownian random processes. Solutions of stochastic equations and systems are analyzed qualitatively.