Transitional dynamics in network game with heterogeneous agents: stochastic case

Алексей Васильевич Королев; Alexey Korolev

doi:10.17076/mgta_2021_1_33

Алексей Васильевич Королев St. Petersburg filial of Higher Scool of Economics
Alexey Korolev St. Petersburg filial of Higher Scool of Economics

DOI: https://doi.org/10.17076/mgta_2021_1_33

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

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.