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Regular version of the site

Book chapter

Game equilibria and transition dynamics in triregular networks

P. 113-128.
Matveenko V., Garmash M., Korolev A. V.

We study game equilibria in a model of production and externalities in network with three 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 what equilibria are possible and under which conditions. We study also which of these equilidria are stable and under which correlations of parameters of the network.
We introduce adjustment dynamics described by differential equations and find conditions of existence and dynamical stability of equilibria in regular networks with three types of agents.