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Complexity applications in Economics

The objective of complexity work in financial economics is to investigate the emergence of complex macroscopic market dynamics out of the individual traders' microscopic interactions [1]. Their main tool is the complex multi-agent modeling.

What can complexity offer economics?

The multi-agent modeling approach permits a departure from the analytically fortified towers of rational expectations equilibrium models. It allows the investigation of markets with realistically imperfect investors, rather than markets composed of perfectly rational 'homo-economicus'agents. In the words of Economics Nobel Laureate Harry Markowitz;

'' Microscopic Simulation of Financial Markets [14] points us towards the future of financial economics. If we restrict ourselves to models which can be solved analytically, we will be modelling for our mutual entertainment, not to maximize explanatory or predictive power.'.

Rational expectations equilibrium theory is to be complemented by stochastic models of agents with limited information, bounded rationality, subjective and limited memory, and finite computational capability. In return, these agents will be endowed with learning, evolutionary and natural selection features [15-17].

Very dramatic effects have been studied in systems where the new information/product/ strategy, rather than being universally broadcasted, flows only among individuals that are in direct binary interaction. In this case, there exists a 'critical density' of potential joiners below which the information/novelty/ trend does not propagate throughout the system [18]. To get an idea of the strength of this effect note that there are well-known conditions [19] where more then half of the individuals are potential joiners and yet the trend does not reach even 1% of its potential adopting community. This effect is currently confronted successfully with real market data.

What does Economics offer to complexity?

The stock market is the largest, most well-tuned, efficient and well-maintained emergence laboratory in the world, with the most dense and precise measurements performed, recorded, transmitted, stored and documented flawlessly on extremely reliable databases. Add to this the potential relevance to the most money-saturated human activity in the world and we obtain a very promising vast area to exercise our drives for understanding.

As opposed to elementary particle field theory, in which the microscopic 'bare' interactions are to be inferred from the emerging dynamics, or to cosmology where the emerging macroscopic features are unknown at the largest scales, in financial markets both the microscopic operations and the macroscopic trends are fully documented. The old dream of Boltzmann and Maxwell of following in detail the emergence of macroscopic irreversibility, generic universal laws and collective robust features from microscopic simple elementary interactions can now be fully realized with the help of this wonderful immense thermodynamic machine where the Maxwell demons are human size and (Adam Smith's [20]) invisible hand is more visible than ever.

Are we in danger of over-simplifying?

Quite the contrary! The multi-agent modeling techniques allow the long awaited injection of behaviorally realistic 'souls' [21] into the 'rational' financial agents. Rather than 'dehumanizing' the trader models, we introduce the possibility of integrating into them the data from a wide range of neighboring behavioral sciences.

The motivation of these efforts is not a belief that everything can be reduced to physics, to mechanics. The objective is to identify those things that can be reduced, and expose those that cannot be reduced.

The macroscopic financial lab which is the stock/futures/money-market may be considered as a macroscopic human behavior lab capable of dealing round the clock, simultaneously, with millions of subjects around the world. Those subjects are naturally motivated and act in natural yet highly structured conditions. All subjects around the world are exposed to very uniform stimuli (the information appearing on their standard trader screens) in identical procedural order. Their decisions (buy-sell orders) are taken freely, and their content and relative timing are closely monitored and documented in a way which makes the data immediately available for massive computer processing and for comparison with the theoretical (or microscopic simulation) predictions.

Practical benefits

Understanding, monitoring and managing the dynamics of financial markets is of crucial importance: the lives of most individuals in Western society depend on these dynamics. Market dynamics affect not only investments and savings in pension plans, but also the real business cycle, employment, growth and ultimately the daily functioning of our society.

Understanding and regulating the dynamics of financial markets is in some ways similar to predicting and monitoring weather or road traffic, and at least as important. Several groups have attempted to develop certain prediction capabilities about the financial markets; however, universally accepted successful methods or results have not been published until now. Some groups claim that they entrusted their know-how to private profit-oriented companies. Fortunately this has not yet led to macroscopic disasters, but it is certainly a matter of top priority that the public and the authorities in charge of economic stability will have at their disposal standard reliable tools of monitoring, analysis and intervention. Settling for less than that would be like leaving traf-fic control to the trucking companies.

The next objective should be to create the human, methodological and technical capabilities to transform the monitoring, prediction and regulation of stock markets into a reliable activity at a level comparable to the current capabilities of estimating urban traffic: one cannot predict individual car accidents but one can predict, based on the current data, the probable behavior of the system as a whole. Such a prediction ability allows optimization of system design as well as on-line intervention to avert unwanted jams etc. Moreover, one can estimate the effect of unpredictable events and prepare the reaction to them.

Importance of Finance Market studies for the Multi-Agent Complexity

The stock market is the ideal space for the strategic opening to a new kind of science such as, for example, articulated and led by Anderson [25] for the last three decades: it offers a perfectly rigorous experimental and theoretical research framework while avoiding the artificial traditional boundaries (and the resulting restrictions and limitations) between the over-populated feuding kingdoms of the 'exact' sciences continent.

The successful study of stock market dynamics requires a synthesis of knowledge and techniques from different domains: financial economics, psychology, sociology, physics and computer science. These fields have very different 'cultures': different objectives, criteria of success, techniques and language. Bringing people from these disciplines together is not enough—a profound shift in their way of thinking is necessary.

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