Game Equilibria and Transition Dynamics in Complete Networks and in a Triangle with Heterogeneous Agents

Abstract

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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Correspondence to M. V. Garmash or X. A. Kaneva.

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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

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Keywords

  • network
  • game in network
  • Nash equilibrium
  • externality
  • unification dynamics
  • dynamic stability
  • productivity
  • triangle
  • heterogeneous agents