Geodesic
Adjustment dynamics in a regular stochastic network
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 13 (2021) no. 4, pp. 72-92.

Voir la notice de l'article provenant de la source Math-Net.Ru

Stochastic parameters are introduced in the network game model with production and knowledge externalities. The original model was formulated by V. D. Matveenko and A.V. Korolev and was a generalization of a simple two-period Romer model transferred to networks. Each economic agent has an initial supply of goods, which in the first period it can use for consumption and for investment in knowledge. In the second period, it receives the results of its investments, but these results depend not only on the size of its investments, but also on the total investments of its neighbors in the network. The target function of each agent depends on its consumption in both periods. The concept of "Jacobian" equilibrium in this model is concretized as "Nash equilibrium with externalities". This equilibrium differs from the usual Nash equilibrium in that each agent, when making a decision about the size of its investment, considers the environment (which includes its investment) as exogenously defined. The main results of the basic deterministic model are presented, in particular, the definition of the adjustment dynamics under continuous consideration. In this paper, we consider a stochastic generalization of the basic model. Agent productivity has not only deterministic, but also Brown components. The explicit solution of stochastic differential equations describing the adjustment dynamics is obtained. In previous studies, the transition dynamics between stable equilibrium states in the network was considered in the deterministic case. It turns out that the boundaries of various scenarios of agent behavior (and these scenarios themselves) in the stochastic case change significantly compared to the deterministic case. In conclusion, possible further statements of the problem are considered.
Keywords: network games, differential games, regular network, Brownian process, Nash equilibrium, adjustment dynamics, stochastic differential equations. 
@article{MGTA_2021_13_4_a3,
     author = {Marianna V. Matushkina and Xenia V. Soboleva},
     title = {Adjustment dynamics in a regular stochastic network},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {72--92},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2021_13_4_a3/}
}
TY  - JOUR
AU  - Marianna V. Matushkina
AU  - Xenia V. Soboleva
TI  - Adjustment dynamics in a regular stochastic network
JO  - Matematičeskaâ teoriâ igr i eë priloženiâ
PY  - 2021
SP  - 72
EP  - 92
VL  - 13
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MGTA_2021_13_4_a3/
LA  - ru
ID  - MGTA_2021_13_4_a3
ER  - 
%0 Journal Article
%A Marianna V. Matushkina
%A Xenia V. Soboleva
%T Adjustment dynamics in a regular stochastic network
%J Matematičeskaâ teoriâ igr i eë priloženiâ
%D 2021
%P 72-92
%V 13
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MGTA_2021_13_4_a3/
%G ru
%F MGTA_2021_13_4_a3
Marianna V. Matushkina; Xenia V. Soboleva. Adjustment dynamics in a regular stochastic network. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 13 (2021) no. 4, pp. 72-92. http://geodesic.mathdoc.fr/item/MGTA_2021_13_4_a3/

[1] Belopolskaya Ya. I., Stokhasticheskie differentsialnye uravneniya, Lan, SPb., 2019

[2] Bulinskii A. V., Shiryaev A. N., Teoriya sluchainykh protsessov, FIZMATLIT, M., 2005

[3] Gikhman I. I., Skorokhod A. V., Stokhasticheskie differentsialnye uravneniya, Naukova dumka, Kiev, 1968

[4] Oksendal B., Stokhasticheskie differentsialnye uravneniya, Mir, M., 2003

[5] Borodin A. N., Salminen P., Handbook of Brownian Motion. Facts and Formulae, Birkhauser Verlag, Basel–Boston–Berlin, 1996 | Zbl

[6] Bramoullé Y., Kranton R., D'Amours M., “Strategic interaction and networks”, Amer. Econ. Review, 104:3 (2014), 898–930 | DOI

[7] Galeotti A., Goyal S., Jackson M. O., Vega-Redondo F., Yariv L., “Network games”, Review of Econ. Studies, 77 (2010), 218–244 | DOI | Zbl

[8] Garmash M. V., Kaneva X. A., “Game equilibria and adjustment dynamics in full networks and in triangle with heterogeneous agents”, Automation and Remote Control, 81:6 (2020), 1149–1165 | DOI | Zbl

[9] Jackson M. O., Zenou Y., “Games on networks”, Handbook of game theory, v. 4, eds. Young P., Zamir S., 2014, 95–163

[10] Lamperti J., Stochastic processes, Springer-Verlag, New York, 1977 | Zbl

[11] Martemyanov Y. P., Matveenko V. D., “On the dependence of the growth rate on the elasticity of substitution in a network”, Int. Journal of Process Ma-nagement and Benchmarking, 4:4 (2014), 475–492 | DOI

[12] Matveenko V. D., Korolev A. V., “Network game with production and knowledge externalities”, Contributions to Game Theory and Management, 8 (2015), 199–222

[13] Matveenko V., Korolev A., Zhdanova M., “Game equilibria and unification dy-namics in networks with heterogeneous agents”, Int. Journal of Engineering Business Management, 9 (2017), 1–17 | DOI

[14] Matveenko V. D., Korolev A. V., “Knowledge externalities and production in network: game equilibria, types of nodes, network formation”, Int. Journal of Computational Economics and Econometrics, 7:4 (2017), 323–358 | DOI

[15] Matveenko V., Garmash M., Korolev A., “Game Equilibria and Transition Dynamics in Networks with Heterogeneous Agents”, Frontiers of Dynamic Games, Chapter 10, eds. L.A. Petrosyan, V.V. Mazalov, N.A. Zenkevich, Birkhauser/Springer, 2018, 165–188 | DOI | Zbl

[16] Romer P. M., “Increasing returns and long-run growth”, The Journal of Political Economy, 94 (1986), 1002–1037 | DOI