Collective Intelligence for Control of Distributed Dynamical Systems

TL;DR

This paper presents a mathematical framework for configuring distributed dynamical systems, like the minority game, to optimize collective behavior and achieve global goals by minimizing energy functions.

Contribution

It introduces a theory for configuring nodes in distributed systems to avoid conflict and optimize collective outcomes, demonstrated on the minority game.

Findings

System designed with the theory performs nearly optimally.

The framework applies when global goals are expressed as energy minimization.

Nodes as local energy minimizers lead to effective collective behavior.

Abstract

We consider the El Farol bar problem, also known as the minority game (W. B. Arthur, ``The American Economic Review'', 84(2): 406--411 (1994), D. Challet and Y.C. Zhang, ``Physica A'', 256:514 (1998)). We view it as an instance of the general problem of how to configure the nodal elements of a distributed dynamical system so that they do not ``work at cross purposes'', in that their collective dynamics avoids frustration and thereby achieves a provided global goal. We summarize a mathematical theory for such configuration applicable when (as in the bar problem) the global goal can be expressed as minimizing a global energy function and the nodes can be expressed as minimizers of local free energy functions. We show that a system designed with that theory performs nearly optimally for the bar problem.