Equilibria in Networks with Production and Knowledge Externalities

  • Vladimir MatveenkoEmail author
  • Alexei Korolev
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 156)


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.


Network Structure of network Network game Nash equilibrium  Externality Network formation 



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


  1. 1.
    Azariadis, C.,  Chen, B.-L.,  Lu, C.-H.,  Wang, Y.-C.: A two-sector model of endogenous growth with leisure externalities. J. Econ. Theory 148, 843–857 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bramoullé, Y.,  Kranton, R.: Public goods in networks. J. Econ. Theory 135, 478–494 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bulow, J., Geanakoplos, J., Klemperer, P.: Multimarket oligopoly: strategic substitutes and complements. J. Polit. Econ. 93 (3), 488–511 (1985)CrossRefGoogle Scholar
  4. 4.
    Galeotti, A.,  Goyal, S.,  Jackson, M.O.,  Vega-Redondo, F.,  Yariv, L.: Network games. Rev. Econ. Stud. 77, 218–244 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Grossman, G., Maggi, G.: Diversity and trade. Am. Econ. Rev. 90, 1255–1275 (2000)CrossRefGoogle Scholar
  6. 6.
    Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton (2008)zbMATHGoogle Scholar
  7. 7.
    Jackson, M.O., Zenou, Y.: Games on networks. In: Young P., Zamir S. (eds.) Handbook of Game Theory, vol. 4, pp. 95–164. Elsevier Science, North-Holland (2015)Google Scholar
  8. 8.
    Jacobs, J.: The Economy of Cities. Random House, New York (1969)Google Scholar
  9. 9.
    Lucas, R. E.: On the mechanics of economic development. J. Monetary Econ. 22, 3–42 (1988)CrossRefGoogle Scholar
  10. 10.
    Martemyanov, Y.P., Matveenko, V.D.: On the dependence of the growth rate on the elasticity of substitution in a network. Int. J. Process Manag. Benchmark. 4 (4), 475–492 (2014)CrossRefGoogle Scholar
  11. 11.
    Milgrom, P., Roberts, J.: The economics of modern manufacturing: technology, strategy, and organisation. Am. Econ. Rev. 80, 511–518 (1990)Google Scholar
  12. 12.
    Milgrom, P., Roberts, J.: Complementarities and systems: understanding Japanese economic organisation. Estud. Econ. 9, 3–42 (1994)Google Scholar
  13. 13.
    Romer, P. M.: Increasing returns and long-run growth. J. Polit. Econ. 94, 1002–1037 (1986)CrossRefGoogle Scholar
  14. 14.
    Topkis, D.M.: Supermodularity and Complementarity. Princeton University Press, Princeton (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsSt. PetersburgRussia

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