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.

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

“…Following [12], we introduce the dynamics caused by a small deviation from an equilibrium or by the union of separate networks each of which was in an equilibrium. The dynamics will be modeled in the following way.…”

“…Sections 2 and 3 contain the well-known results obtained by Matveenko and Korolev; for example, see [11,12]. Definitions 4.1 and 5.1 that are given at the beginning of Sections 4 and 5, respectively, also ideologically follow the paper [12].…”

“…In the paper [12], the heterogeneity of agents and unification dynamics were incorporated into the two-period consumption-investment model with network externalities [11]. It was assumed that there are two types of agents characterized by different productivities, but only the case of complete networks was studied therein.…”

“…Following [12], we introduce unification dynamics in a triangle and study the dynamics of transition into a new equilibrium. The problems addressed below are the analysis of possible equilibria in a triangle and the establishment of conditions under which these equilibria are stable.…”

Measuring economic growth using production possibility frontier under Harrod neutrality

“…However, investigating mutual relationships of agents is an important issue for a productivity analysis. As an example, Matveenko et al 41 show three types of behaviour of agents whose productivities are different, based on a model of production and externalities in network with two types of agents.…”