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

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. These theoretical findings offer new insights into several economic applications.

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