Variational Inequalities, Nash Equilibrium Problems and Applications: Unification Dynamics in Networks
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 projectionbased
method for solving variational inequalities for the description of adjustment
dynamics in networks.