Transitional dynamics in network game with heterogeneous agents: stochastic case

Alexey V. Korolev

St. Petersburg filial of Higher Scool of Economics

Abstract: In this paper, stochastic parameters are introduced into the network games model with production and knowledges externalities. This model was formulated by V. Matveenko and A. Korolev and generalized two-period Romer model. Agents' productivities have deterministic and Wiener components. The research represents the dynamics of a single agent and the dynamics in a triangle which occurs in the process of unifying agents. Explicit expressions of the dynamics of a single agent and dyad agents in the form of Brownian random processes were obtained. A qualitative analysis of the solutions of stochastic equations and systems was carried out.

Keywords: network games, differential games, Nash equilibrium, Brounian motion, stochastic differential equations, Ito's Lemma, heterogeneous agents, productivity.

UDC: 519.83, 519.86
BBK: 22.18

Received: 04.10.2020
Revised: 21.12.2020
Accepted: 09.03.2021