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Equilibria in Networks with Production and Knowledge Externalities

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Models, Algorithms and Technologies for Network Analysis (NET 2014)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 156))

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Abstract

We consider a game equilibrium in a network in each node of which an economy is described by the simple two-period model of endogenous growth with production and knowledge externalities. Each node of the network obtains an externality produced by the sum of knowledge in neighbor nodes. Uniqueness of the inner equilibrium is proved. Three ways of behavior of each agent are distinguished: active, passive, and hyperactive. Behavior of agents in dependence on received externalities is studied. It is shown that the equilibrium depends on the network structure. We study the role of passive agents and, in particular, possibilities of connection of components of active agents through components of passive agents. Changes of the equilibrium under changes in the network structure are studied. It is shown that appearance of a new link, as a rule, leads to decrease of knowledge in all nodes, but sometimes knowledge in some nodes increases. A notion of type of node is introduced and classification of networks based on this notion is provided. It is shown that the inner equilibrium depends not on the size of network but on its structure in terms of the types of nodes, and in similar networks of different size agents of the same type behave in similar way.

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Notes

  1. 1.

    The term “agent” is used in economics, while the term “actor” is used in management, sociology, and politology. We speak further about “agents” despite results of our work may have applications in analysis of economic as well as social and political relations.

  2. 2.

    Since b > a, the necessary and sufficient condition (53) follows from simple sufficient condition a > 3∕10.

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Acknowledgements

The research was partially supported by Russian Foundation for Basic Research (projects 14-01-00448 and 14-06-00253).

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Authors and Affiliations

  1. National Research University Higher School of Economics, 16 Soyuza Pechatnikov Street, St. Petersburg, 190121, Russia

    Vladimir Matveenko & Alexei Korolev

Authors
  1. Vladimir Matveenko
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  2. Alexei Korolev
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Corresponding author

Correspondence to Vladimir Matveenko .

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Editors and Affiliations

  1. Laboratory of Algorithms and Technologies for Network Analysis (LATNA), National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A. Kalyagin

  2. Laboratory of Algorithms and Technologies for Network Analysis (LATNA), National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Petr A. Koldanov

  3. Department of Industrial and System Engineering, Center for Applied Optimization University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Matveenko, V., Korolev, A. (2016). Equilibria in Networks with Production and Knowledge Externalities. In: Kalyagin, V., Koldanov, P., Pardalos, P. (eds) Models, Algorithms and Technologies for Network Analysis. NET 2014. Springer Proceedings in Mathematics & Statistics, vol 156. Springer, Cham. https://doi.org/10.1007/978-3-319-29608-1_20

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