Visualizing the Invisible Hand of Markets: Simulating Complex Dynamic Economic Interactions

• Date: 01 April 2015
• Author: Klaus Jaffé
• DOI: http://doi.org/10.1002/isaf.1368
• Published date: 01 April 2015

VISUALIZING THE INVISIBLE HAND OF MARKETS:

SIMULATING COMPLEX DYNAMIC ECONOMIC INTERACTIONS

KLAUS JAFFÉ*

Universidad Simón Bolívar, Caracas,Venezuela

SUMMARY

In complex systems, many different parts interact in nonobvious ways. Traditional research focuses on a few or a

single aspect of the problem so as to analyse it with the tools available. To get a better insight of phenomena that

emerge from complex interactions, we need instruments that can analyse simultaneously complex interactions be-

tween many parts. Here, a simulator modelling different types of economies is used to visualize complex quanti-

tative aspects that affect economic dynamics. The main conclusions are: (1) relatively simple economic settings

produce complex nonlinear dynamics and, therefore, linear regressions are often unsuitable to capture complex

economic dynamics; (2) flexible pricing of goods by individual agents according to their microenvironment in-

creases the health and wealth of the society, but asymmetries in price sensitivity between buyers and sellers in-

crease price inflation; (3) prices for goods conferring risky long-term benefits are not tracked ef ficiently by

simple market forces; (4) division of labour creates synergies that improve enormously the health and wealth of

the society by increasing the efficiency of economic activity; (5) stochastic modelling improves our understanding

of real economies, and didactic games based on them might help policy-makers and nonspecialists in grasping the

complex dynamics underlying even simple economic settings. Copyright © 2015 John Wiley & Sons, Ltd.

Keywords: Sociodynamica; non-linear; chaos; bioeconomy; evolution

1. INTRODUCTION

Adam Smith (1977[1776]) and Friedrich Hayek (1961), among many others, assigned extraordinary

importance to hidden properties of markets. They assumed the existence of poorly understood complex

market mechanisms upon which modern economies are built. These mechanisms and the phenomena

they produce are not easily grasped analytically because of their extraordinary complexity. Mathemat-

ics, the language we use to ask questions to nature, has expanded the limits of economic analytical

power since Hayek wrote about the ‘Economic Calculus’and Smith about ‘The Invisible Hand’.We

now are capable of viewing economies with more powerful tools that allow for a more rigorous analysis

of complex features formerly regarded as off limits to rational reductionist methods by economists.

These tools allow one to produce multidimensional radiographies of an economy.They include ‘cellular

automata’(Axelrod, 1984), ‘active walks’(Lam, 2005, 2006) and computer simulations. Specifically,

agent-based modelling (ABM) allows one to simulate very complex phenomena in economics (e.g.

Prietula & Carley, 1994; Kochugovindan & Vriend, 1998; Magliocca, Brown, & Ellis, 2014). ABM

simulations can easily be made so complex as to be beyond our understanding, becoming unpredict-

able. Thus, in order to remain useful, we have to limit the complexity of ABM so as not to trespass this

edge of chaos. The mathematically relevant challenge is to find the simplest representation of reality

that is able to capture the problem to be studied.

* Correspondence to: Klaus Jaffé, Universidad Simon Bolivar, Apartado Postal 89000, Caracas 1080, Venezuela. E-mail: kjaffe@usb.ve

Copyright © 2015 John Wiley & Sons, Ltd.

INTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE AND MANAGEMENT

Intell. Sys. Acc. Fin. Mgmt. 22, 115–132 (2015)

Published online 12 May 2015 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/isaf.1368

Sociodynamica is an agent-based simulation model, purposely built for analysing economic

microdynamics. It is based on classical monetary economic principles (Gurley & Shaw, 1960; Wray,

1996) and builds virtual societies of agents that collect and trade two types of heterogeneously distrib-

uted resources. It can be made as complex as one would wish, but in order to comply with the maxi-

mum entropy principle (Jaynes, 1957) we want to keep the problem simple and advance our

knowledge in small steps. The aim here is to build the simplest mathematical construct that still reflects

aspects of the economic dynamics that are fundamental to modern complex economies. Specifically, we

want to reproduce phenomena, such as the emergence of the ‘Invisible Hand’coined by Adam Smith.

Sociodynamica is specifically aimed to visualize the process of emergence of new macro phenomena

from the microscopic social interaction of agents and has been in continuous development, starting

from Biodynamica, for the last 20 years. A large number of alternative agent-based simulation models

for economic problems are available—see Tesfatsion (2014). For example, ‘Sugar-scape’, an agent-

based model developed independently by Axelrod (1984), and the model developed by Axtell (2005)

are very similar to Sociodynamica. Eventually, repeating the simulations presented here with other

agent-based models, and devising empirical studies based on these simulations, should add confidence

to the results presented and advance our understanding of complex markets.

2. METHOD

Sociodynamica is a freely available agent-based simulation model written in Visual Basic in which

diverse agents roam a virtual landscape looking for resources. Agents farm and mine for foods and

minerals and trade their surplus according to different economic settings. Sociodynamica assumes that

utility functions in economics are equivalent to fitness functions in biology (Kenrick et al., 2009),

simulating the survival of agents in situations with or without heredity and with or without movement

of agents. Sociodynamica has been used previously to study the effect of altruism and altruistic punish-

ment on aggregate wealth accumulation in artificial societies (Jaffe, 2002a, 2004a, 2008; Jaffe &

Zaballa, 2009, 2010) and in studying the dynamics of complex markets (Jaffe, 2002b, 2004b).

The present model simulated a virtual society of agents that farmed and mined food and minerals

respectively and traded their surplus according to different economic settings. The agents inhabited a

continuous, flat two-dimensional toroidal world (see Figure 2) that was supplied with patches of agri-

cultural land (‘sugar’or ‘food’) and separate nonoverlapping patches of mines (‘spices’or minerals).

Immobile agents were randomly dispersed over this fine-grained virtual landscape. Each time step,

agents that happened to be located over one of the resources acquired a unit of the corresponding re-

source, accumulating wealth, either as sugar or food (G

1

) and/or as spices or minerals (G

2

). Agents

spend a fixed amount of each resource in order to survive, consuming each of them at a basal constant

rate (default value was 0.1 units of the corresponding resource). Both resources were consumed and

metabolized similarly, but food was three times more abundant than minerals (the size of the patch

for minerals was normally set to 100× 100 pixels and for food 300 × 300 pixels). Each patch remained

in the same place during each simulation run and the resources inside them were replenished continu-

ously. Agents perished when they exhausted any of the two resources. The population of agents was

maintained constant by introducing after each time step new agents with randomly assigned initial pa-

rameters. Initial parameters were the type of agent, the random spatial position and the initial amount of

money used to start trading resources (the default initial value was set to 10 units of money). The

amount of money each agent possessed varied according to its trade balances. Agents gained money

when selling food and/or minerals and spent money when buying them.

116 K. JAFFÉ

Copyright © 2015 John Wiley & Sons, Ltd. Intell. Sys. Acc. Fin. Mgmt., 22, 115–132 (2015)

DOI: 10.1002/isaf