The game equilibrium in networks described by the two-period Romer model of endogenous growth with production and knowledge externalities is considered. In the first period, each agent can invest some share of his resources. In the second period, the consumption depends on his investment and productivity as well as the investments of his network neighbors. The unification dynamics are described by a system of difference equations. For a complete network with an arbitrary number of homogeneous agents and also for a triangle (a complete network with three types of agents possessing different productivities), possible equilibria are studied and their dynamic stability under different combinations of the game parameters is analyzed.
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Acemoglu, D. and Robinson, J.A., Why Nations Fall: The Origins of Power, Prosperity, and Poverty, New York: Crown, 2012.
Ballester, C., Calvo-Armengol, A., and Zenou, Y., Who’s Who in Networks. Wanted: The Key Player, Econometrica, 2006, vol. 74, no. 5, pp. 1403–1417.
Bramoullé, Y. and Kranton, R., Public Goods in Networks, J. Economic Theory, 2007, vol. 135, pp. 478–494.
Bramoullé, Y., Kranton, R., and D’Amours, M., Strategic Interaction and Networks, Am. Economic Rev., 2014, vol. 104, no. 3, pp. 898–930.
Galeotti, A., Goyal, S., Jackson, M.O., Vega-Redondo, F., and Yariv, L., Network Games, Rev. Economic Stud., 2010, vol. 77, pp. 218–244.
Goyal, S., Connections: An Introduction to the Economics of Networks, Princeton: Princeton Univ. Press, 2010.
Jackson, M.O., Social and Economic Networks, Princeton: Princeton Univ. Press, 2008.
Jackson, M.O. and Zenou, Y., Games on Networks, in Handbook of Game Theory, Young, P. and Zamir, S., Eds., Amsterdam: Elsevier Science, 2014, vol. 4, pp. 95–163.
Lucas, R., On the Mechanics of Economic Development, J. Monet. Econ., 1988, vol. 2, no. 1, pp. 3–42.
Martemyanov, Y.P. and Matveenko, V.D., On the Dependence of the Growth Rate on the Elasticity of Substitution in a Network, Int. J. Process Manage. Benchmarking, 2014, vol. 4, no. 4, pp. 475–492.
Matveenko, V.D. and Korolev, A.V., Network Game with Production and Knowledge Externalities, Contrib. Game Theory Manage., 2015, no. 8, pp. 199–222.
Matveenko, V.D., Korolev, A.V., and Zhdanova, M.O., Game Equilibria and Unification Dynamics in Networks with Heterogeneous Agents, Int. J. Eng. Business Manag., 2017, vol. 9, pp. 1–17.
Naghizadeh, P. and Liu, M., Provision of Public Goods on Networks: On Existence, Uniqueness, and Centralities, IEEE Trans. Network Sci. Eng., 2018, vol. 5, no. 3, pp. 225–236.
Romer, P.M., Increasing Returns and Long-Run Growth, J. Political Economy, 1986, vol. 94, pp. 1002–1037.
Russian Text © The Author(s), 2018, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2018, No. 2, pp. 3–26.
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Garmash, M.V., Kaneva, X.A. Game Equilibria and Transition Dynamics in Complete Networks and in a Triangle with Heterogeneous Agents. Autom Remote Control 81, 1149–1165 (2020). https://doi.org/10.1134/S0005117920060144
- game in network
- Nash equilibrium
- unification dynamics
- dynamic stability
- heterogeneous agents