Variational Inequalities, Nash Equilibrium Problems and Applications: Unification Dynamics in Networks

  • Vladimir Matveenko
  • Maria Garmash
  • Alexei Korolev
Part of the Static & Dynamic Game Theory: Foundations & Applications book series (SDGTFA)


We study game equilibria in a model of production and externalities in network with two types of agents who possess different productivities. Each agent may invest a part of her endowment (for instance, time or money) on the first stage; consumption on the second period depends on her own investment and productivity as well as on the investments of her neighbors in the network. Three ways of agent’s behavior are possible: passive (no investment), active (a part of endowment is invested) and hyperactive (the whole endowment is invested). We introduce adjustment dynamics and study consequences of junction of two regular networks with different productivities of agents. We use the projection-based method for solving variational inequalities for the description of adjustment dynamics in networks.


Network Nash equilibrium Externality Productivity Adjustment dynamics Variational inequality 



The research is supported by the Russian Foundation for Basic Research (project 17-06-00618)


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vladimir Matveenko
    • 1
  • Maria Garmash
    • 1
  • Alexei Korolev
    • 1
  1. 1.National Research University Higher School of Economics at St. PetersburgSt. PetersburgRussia

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