The Network Topology of Locally Interacting Agents and System-Level Distributions of Agent Actions

Abstract

This work develops the mathematics that underlies many agent-based models and multi-agent systems, both of which could only previously be studied by computer simulation. It also introduces complexity into the study of economic systems while retaining closed-form analysis, and it establishes new results in the area of network-based learning. In essence, this work takes an economic system with N locally interacting agents and from it, constructs a system-level distribution of agent actions. The N agents possess a binary-valued attribute, and their decision-making depends on the local frequency of the attribute, as defined by an underlying network topology. There is an outside observer at the system level who knows both the global frequency of the attribute and agents' network topology, but not the configuration of the binary-valued attribute among agents. For every population size, global frequency of the attribute, and feasible network topology, this work constructs system-level distributions of agent actions. This work also solves the converse problem, that of inferring the network's topology from aggregate data. These theoretical findings offer new insights into the following set of applications: political election outcomes that depend on locally formed macroeconomic sentiments; the existence of a negative multiplier on a population's aggregate action following a strictly non-negative shock (stimulus) to the initial action of every agent; and dynamic deposit and withdrawal behavior for agents in a banking setting and how the underlying agent interaction network shapes risk management policies for the bank.