Game equilibria and unification dynamics in networks with heterogeneous agents

Abstract

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 (it may be, for instance, time or money) in the first of two time periods; consumption in 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). For star network with different productivities of agents in the center and in the periphery, we obtain conditions for existence of inner equilibrium (with all active agents) and study comparative statics. We introduce adjustment dynamics and study consequences of junction of two complete networks with different productivities of agents. In particular, we study how the behavior of nonadopters (passive agents) changes when they connect to adopters (active or hyperactive) agents.