The applicability of complex systems theory in economics is evaluated and compared with standard approaches to economic theorizing based upon constrained optimization. A complex system is defined in the economic context and differentiated from complex systems in physiochemical and biological settings. It is explained why it is necessary to approach economic analysis from a network, rather than a production and utility function perspective, when we are dealing with complex systems. It is argued that much of heterodox thought, particularly in neo-Schumpeterian and neo-Austrian evolutionary economics, can be placed within a complex systems perspective upon the economy. The challenge is to replace prevailing ‘simplistic’ theories, based in constrained optimization, with ‘simple ’ theories, derived from network representations in which value is created through the establishment of new connections between elements.

Stock markets are very important in modern societies and their behaviour have serious implications in a wide spectrum of the world’s population. Investors, governing bodies and the society as a whole could benefit from better understanding of the behaviour of stock markets. The traditional approach to analyze such systems is the use of analytical models. However, the complexity of financial markets represents a big challenge to the analytical approach. Most analytical models make simplifying assumptions, such as perfect rationality and homogeneous investors, which threaten the validity of analytical results. This motivates the use of alternative methods. For those reasons, the study of such markets is a fertile field to use the agent-based methodology. In this work, we developed an artificial financial market and used it to study the behaviour of stock markets. In this market, we model technical, fundamental and noise traders. The technical traders are non-simple genetic programming based agents that co-evolve (by means of their fitness function) by predicting investment opportunities in the market using technical analysis as the main tool. Such traders are equipped with

Note: The Discussion Papers in this series are prepared by members of the Department of Economics, University of Essex, for private circulation to interested readers. They often represent preliminary reports on work in progress and should therefore be neither quoted nor referred to in published work without the written consent of the author. 1

modelling: Asset markets, economic networks, computational mechanism design and evolutionary game dynamics 1. Background This Special Issue consists mostly of the work presented at the Tenth Workshop on Economic Heterogeneous Interacting Agents (WEHIA 2005) hosted by the Centre for Computational Finance and Economic Agents of the University of Essex, UK. The collection reports on advances in an exciting and fast growing subfield of economics, with replication and analysis of markets and other socio-economic environments with interacting, often heterogeneous, artificial and human agents as the major themes. The conference also honoured the contributions of Benoit Mandelbrot who delivered a keynote address on the statistical signatures of complex dynamical systems characterized by non-Gaussian phenomena of fat tails and fractal nature of volatility – themes that resonate in a number of contributions included here. The subfield that comprises these papers is variously referred to as agent-based computational economics (ACE) and Economic Science for Heterogeneous Interacting Agents (ESHIA). This field has built on advances in complex adaptive systems (CAS) and computer hardware and software that are outlined below. 1.1. Advances in complexity sciences The formal results on the limits of computability and logical deduction, and the von Neumann-inspired investigation (1970) of artificial evolution have led to the growth of complexity sciences and the interdisciplinary study of complex adaptive systems. CAS is closely related to self-referential decision problems that can be proven not to have a unique and effective procedure for finding solutions. Decision

Abstract. We study ensembles of similar systems under load of environmental factors. The phenomenon of adaptation has similar properties for systems of different nature. Typically, when the load increases above some threshold, then the adapting systems become more different (variance increases), but the correlation increases too. If the stress continues to increase then the second threshold appears: the correlation achieves maximal value, and start to decrease, but the variance continue to increase. In many applications this second threshold is a signal of approaching of fatal outcome. This effect is supported by many experiments and observation of groups of humans, mice, trees, grassy plants, and on financial time series. A general approach to explanation of the effect through dynamics of adaptation is developed. H. Selye introduced “adaptation energy ” for explanation of adaptation phenomena. We formalize this approach in factors – resource models and develop hierarchy of models of adaptation. Different organization of interaction between factors (Liebig’s versus synergistic systems) lead to different adaptation dynamics. This gives an explanation to qualitatively different dynamics of correlation under different types of load and to some deviation from the typical reaction to stress. In addition to the “quasistatic ” optimization factor – resource models, dynamical models of adaptation are developed, and a simple model (three variables) for adaptation to one factor load is formulated explicitly.

We study the dynamics of correlation and variance in systems under the load of environmental factors. A universal effect in ensembles of similar systems under load of similar factors is described: in crisis, typically, even before obvious symptoms of crisis appear, correlation increases, and, at the same time, variance (and volatility) increases too. After the crisis achieves its bottom, it can develop into two directions: recovering (both correlations and variance decrease) or fatal catastrophe (correlations decrease, but variance not). This effect is supported by many experiments and observation of groups of humans, mice, trees, grassy plants, and on financial time series. A general approach to explanation of the effect through dynamics of adaptation is developed. Different organization of interaction between factors (Liebig’s versus synergistic systems) lead to different adaptation dynamics. This gives an explanation to qualitatively different dynamics of correlation under different types of load.

Shipping as a complex adaptive system: A new approach in understanding international trade