Dynamic network model of production and investment

Authors

  • Vitaly A. Kochevadov St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation https://orcid.org/0009-0001-5432-9317
  • Artem A. Sedakov St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation https://orcid.org/0000-0001-5419-8436

DOI:

https://doi.org/10.21638/11701/spbu10.2023.102

Abstract

The paper studies a dynamic network game that models the competitive behavior of firms in a market. It is assumed that firms, under the condition of simultaneous and independent choice of their actions, implement the behavior that determines their production and investment behavior in each period. The production behavior of the firm reflects the ongoing quantities that it should produce and supply to the market. The investment behavior specifies the ongoing amounts of investment that the firm allocates to the modernization of its production technology in order to prevent it from becoming obsolete. Next, the unit cost is assumed to depend on the firm's investment and the investment of its competitors, which are determined by an exogenous network. Two types of Nash equilibria are characterized: open-loop and feedback. Finally, we analyze the impact of the network and related model parameters on firms' behavior, profits, and competitive advantage.

Keywords:

competition, investment, dynamic game, network, Nash equilibrium

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References

Литература

Jackson M. O. Social and economic networks. Princeton: Princeton University Press, 2008. 520 p.

Galeotti A., Goyal S., Jackson M. O., Vega-Redondo F., Yariv L. Network games // Review of Economic Studies. 2010. Vol. 77. P. 218-244.

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Cellini R., Lambertini L. Dynamic R&D with spillovers: Competition vs cooperation // Journal of Economic Dynamics & Control. 2009. Vol. 33. P. 568-582.

Ballester C., Calv'o-Armengol A., Zenou Y. Who's who in networks. Wanted: The key player // Econometrica. 2006. Vol. 74. N 5. P. 1403-1417.

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References

Jackson M. O. Social and economic networks. Princeton, Princeton University Press, 2008, 520 p.

Galeotti A., Goyal S., Jackson M. O., Vega-Redondo F., Yariv L. Network games. Review of Economic Studies, 2010, vol. 77, pp. 218-244.

Jackson M. O., Zenou Y. Games on networks. Handbook of game theory with economic applications. Eds by P. Young, S. Zamir. Amsterdam, Elsevier Science Publ., 2015, vol. 4, pp. 95-164.

Novikov D. A. Igri i seti [Games and networks]. Matematicheskaya teoriya igr i ee prilozheniya [ Mathematical game theory and applications ], 2010, vol. 2, no. 1, pp. 107-124. (In Russian)

Goyal S., Moraga-Gonzailez J. L. R&D networks. The RAND Journal of Economics, 2001, vol. 32, no. 4, pp. 686-707.

Zhao J., Ni J. A dynamic analysis of corporate investments and emission tax policy in an oligopoly market with network externality. Operations Research Letters, 2020, vol. 49, pp. 81-83.

Cellini R., Lambertini L. Dynamic R&D with spillovers: Competition vs cooperation. Journal of Economic Dynamics & Control, 2009, vol. 33, pp. 568-582.

Ballester C., Calv'o-Armengol A., Zenou Y. Who's who in networks. Wanted: The key player. Econometrica, 2006, vol. 74, no. 5, pp. 1403-1417.

Goyal S., Joshi S. Networks of collaboration in oligopoly. Games and Economic Behavior, 2003, vol. 43, no. 1, pp. 57-85.

Bulow J., Geanakoplos J., Klemperer P. Multimarket oligopoly: strategic substitutes and complements. Journal of Political Economy, 1985, vol. 93, no. 3, pp. 488-511.

Bramoull'e Y., Kranton R. Public goods in networks. Journal of Economic Theory, 2007, vol. 135, pp. 478-494.

Azariadis C., Chen B.-L., Lu C.-H., Wang Y.-C. A two-sector model of endogenous growth with leisure externalities. Journal of Economic Theory, 2013, vol. 148, pp. 843-857.

Martemyanov Y. P., Matveenko V. D. On the dependence of the growth rate on the elasticity of substitution in a network. International Journal of Process Management and Benchmarking, 2014, vol. 4, pp. 475-492.

Milgrom P., Roberts J. The economics of modern manufacturing: technology, strategy, and organization. American Economic Review, 1990, vol. 80, pp. 511-518.

Milgrom P., Roberts J. Complementarities and systems: understanding Japanese economic organization. Estudios Econ'omicos, 1994, vol. 9, pp. 3-42.

Topkis D. M. Supermodularity and complementarity. Princeton, Princeton University Press, 1998, 288 p.

Cournot А. А. Recherches sur les principes mathematiques de la theorie des richesses par Augustin Cournot. Paris, Hachette Press, 1838, 199 p.

Bacsar T., Olsder G. J. Dynamic noncooperative game theory. London, New York, Academic Press, 1995, 511 p.

Petrosyan L. A., Zenkevich N. A., Shevkoplyas E. V. Teoriya igr [ Game theory ]. St. Petersburg, BKhV-Petersburg Publ., 2012, 432 p. (In Russian)

Mazalov V. V. Matematicheskaya teoriya igr i prilozheniya [ Mathematical game theory and applications ]. Moscow, Lan’ Publ., 2017, 448 p. (In Russian)

Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления, Том 19, Выпуск 1, 2023

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Published

2023-04-27

How to Cite

Kochevadov, V. A., & Sedakov, A. A. (2023). Dynamic network model of production and investment. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 19(1), 10–26. https://doi.org/10.21638/11701/spbu10.2023.102

Issue

Vol. 19 No. 1 (2023)

Section

Applied Mathematics

License

Articles of "Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.