The Economy As An Evolving Complex System

Philip W. Anderson

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9780429972478
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

This book proceeds from a meeting at the Santa Fe Institute where economists and physical and biological scientists came together to discuss a conceptual framework incorporating a more appropriate mathematics with a greatly strengthened capacity to deal simultaneously with multiple variables, nonlinearity, incomplete information and dynamical processes.

II. Lectures and Perspectives

W. BRIAN ARTHUR

Dean and Virginia Morrison Professor of Population Studies and Economics. Food Research Institute. Stanford University. Stanford. CA 94305

Self-Reinforcing Mechanisms in Economics

1. PRELIMINARIES

Dynamical systems of the self-reinforcing or autocatalytic type–systems with local positive feedbacks–in physics, chemical kinetics, and theoretical biology tend to possess a multiplicity of asymptotic states or possible “emergent structures.” The initial starting state combined with early random events or fluctuations acts to push the dynamics into the domain of one of these asymptotic states and thus to “select” the structure that the system eventually “locks into.”

My purpose in this paper is to look at corresponding dynamical systems in economics. The literature covers a wide range of topics; therefore, I will not claim to give a complete survey. My aim is to show that the presence of self-reinforcing mechanisms, in very different problems drawn from different sub-fields of economics, gives rise to common themes, common features. I will note analogies with physical and biological systems; and I will illustrate with theory wherever it is available.

Conventional economic theory is built largely on the assumption of diminishing returns on the margin (local negative feedbacks); and so it may seem that positive feedback, increasing-returns-on-the-margin mechanisms ought to be rare. Yet there is a sizeable literature on such mechanisms, much of it dating back to the 1920’s and 1930’s, particularly in international trade theory, industrial organization, regional economics, and economic development. Self-reinforcement goes under different labels in these different parts of economics: increasing returns; cumulative causation; deviation-amplifying mutual causal processes; virtuous and vicious circles; threshold effects; and non-convexity. The sources vary. But usually self-reinforcing mechanisms are variants of or derive from four generic sources: large set-up or fixed costs (which give the advantage of falling unit costs to increased output); learning effects (which act to improve products or lower their cost as their prevalence increases) (Arrow, 1962; Rosenberg, 1982); coordination effects (which confer advantages to “going along” with other economic agents taking similar action); and adaptive expectations (where increased prevalence on the market enhances beliefs of further prevalence).

To fix ideas, consider a concrete example. The video technology Sony Betamax exhibits market self-reinforcement in the sense that increased prevalence on the market encourages video outlets to stock more film titles in Betamax; there are coordination benefits to new purchasers of Betamax that increase with its market share. If Betamax and its rival VHS compete, a small lead in market share gained by one of the technologies may enhance its competitive position and help it further increase its lead. There is positive feedback. If both systems start out at the same time, market shares may fluctuate at the outset, as external circumstances and “luck” change, and as backers maneuver for advantage. And if the self-reinforcing mechanism is strong enough, eventually one of the two technologies may accumulate enough advantage to take 100% of the market. Notice however we cannot say in advance which one this will be.

Of course, we would need a precise formulation of this example to be able to show that one technology or the other must eventually take all of the market. But for the moment, let us accept that conditions exist under which this happens. Notice four properties:

MULTIPLE EQUILIBRIA. In this problem two quite different asymptotic market-share “solutions” are possible. The outcome is indeterminate; it is not unique and predictable.

POSSIBLE INEFFICIENCY. If one technology is inherently “better” than the other (under some measure of economic welfare), but has “bad luck” in gaining early adherents, the eventual outcome may not be of maximum possible benefit. (In fact, industry specialists claim that the actual loser in the video contest, Betamax, is technically superior to VHS.)

LOCK-IN. Once a “solution” is reached, it is difficult to exit from. In the video case, the dominant system’s accrued advantage makes it difficult for the loser to break into the market again.

PATH-DEPENDENCE. The early history of market shares–in part the consequence of small events and chance circumstances–can determine which solution prevails. The market-share dynamics are non-ergodic.

Economists have known that increasing returns can cause multiple equilibria and possible inefficiency at least since Marshall (1891; Book IV, Ch.13 and Appendix H). Modern approaches to multiple equilibria and inefficiency can be found in Arrow and Hahn, 1971, Ch.9; Brown and Heal, 1979; Kehoe, 1985; Scarf, 1981; among others. In this paper I will concentrate on the less familiar properties of lock-in and path-dependence.

Besides these four properties, we might note other analogies with physical and biological systems. The market starts...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Foreword
• I. Introduction and Overview
• II. Lectures and Perspectives
• III. Working Group Summaries
• IV. Final Plenary Discussion
• V. Summaries and Perspectives
• VI. Research Papers
• VII. Appendix
• Index