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Transition dynamics in a network game with heterogeneous agents: the stochastic case. (English. Russian original) Zbl 1489.91053

Autom. Remote Control 83, No. 3, 483-501 (2022); translation from Mat. Teor. Igr Prilozh. 13, No. 1, 102-129 (2021).
Summary: Stochastic parameters are introduced into a model of network games with production and knowledge externalities. The model was formulated by V. D. Matveenko and A. V. Korolev [in: Contributions to game theory and management. Volume VIII. The 8th international conference on game theory and management (GTM 2014), St. Petersburg, Russia, June 25–27, 2014. Collected papers. St. Petersburg: Graduate School of Management, St. Petersburg State University. 199–222 (2015; Zbl 1418.91102)] 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.

MSC:

91A43 Games involving graphs
91A15 Stochastic games, stochastic differential games
91B69 Heterogeneous agent models
60H30 Applications of stochastic analysis (to PDEs, etc.)

Citations:

Zbl 1418.91102
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References:

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