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Standard economics is based on methodological individualism but this does not imply that the individuals play a crucial role in its models. On the contrary, in such a theory the individual is deprived of authentic subjective characteristics and plays no sizeable role as genuine subject. The so called is just a signpost for given preferences that, however, are generally conceived as exogenous and invariant through time. Therefore, the genuine psychological features of the economic agent do not matter.

‘Complexity’ ideas are becoming a hot issue in economics. Originally developed within the natural sciences, complexity theory is now believed by many to be a novel and powerful framework of thought, capable of challenging the fundamental principles sustained by mainstream economics for more than a century. One of its main advocates, David Colander (2000a:31), has written that “Complexity changes everything; well, maybe not everything, but it does change quite a bit in economics”. Also, in a recent issue of a popular scientific magazine, it is suggested that complexity ideas “are beginning to map out a radical and long-overdue revision of economic theory” (). Indeed, the proliferation of publications, journals, summer schools, and conferences on complexity economics during the past few years can hardly pass unnoticed.

Theoretical science generates testable, logical (mathematical) systems of thought that explain or comprehend observations and empirical data that themselves only reflect some properties of some realm of experience. Progress began to occur rapidly when stable, repetitive patterns were discovered, such as the motion of stellar bodies that could be carefully observed and their distances, masses, and velocities measured, and such as the ratios in which various pure substances interacted to form different compound substances.

The existing linear and non-linear techniques of time series analysis (), long dominant within applied mathematics, the natural sciences, and economics, are inadequate when considering chaotic phenomena.

In this paper, interaction among taxpayers in the tax evasion game is considered by means of game theory with learning. This interaction has been largely neglected in the modeling of tax evasion so far, although it brings about results significantly different from those of a conventional model. In case of tax authority commitment to a certain auditing probability, nonzero cheating equilibrium becomes possible. In case of tax authority with no commitment to a certain auditing probability, cycling may occur instead of long-run equilibrium, allowing for explanation of the fluctuations in “honesty” of taxpayers within the model rather than by exogenous parameter shifts.

We need a new stochastic approach to study macroeconomy composed of a large number of stochastically interacting heterogeneous agents. We reject the standard approach to microfoundation of macroeconomics as misguided, mainly because the framework of intertemporal optimization formulation for representative agents is entirely inadequate to serve as microfoundations of macroeconomics of stochastically interacting microeconomic units.

The behavior of traffic agents is an important topic of recent discussions in social and economic sciences (). The methods are generally based on the Focker Planck equation or master equations (, ). The present investigations are based on the statistics of binary decisions with constraints. This method is known as the Lagrange LeChatelier principle of least pressure in many-decisions systems (, ). The results are compared to data for traffic violations and other criminal acts like shop lifting, theft and murder.

In describing dynamics of classical bodies one uses systems of differential equations (Newton laws). Increasing the number of interacting bodies requires finer time scales and heavier computations. Thus one often takes a statistical approach (e.g. Statistical Mechanics, Markov Chains, Monte Carlo Simulations) which sacrifices the details of the event-by-event causality. The main assumption is that each event is determined only by events immediately preceding it rather than events in the arbitrary past. Moreover, time is often divided in slices and the various cause and effect events are assumed to take place in accordance with this arbitrary slicing. The dynamics of certain economic systems can be expressed similarly. However, in many economic systems, the dynamics is dominated by specific events and specific reactions of the agents to those events. Thus, to keep the model meaningful, causality and in particular the correct ordering of events has to be preserved rigorously down to the lowest time scale.

Global bifurcations in dynamical systems are of considerable interest because they can lead to the creation of chaotic behaviour []. Global bifurcations are to be distinguished from local bifurcations around an unstable periodic solution. Typically, they occur when a homoclinic point is created. A homoclinic point is an intersection point between the stable and the unstable manifold of a steady state saddle point on the Poincaré section of a, at least, 3D flow. The presence of a homoclinic point implies a complicated geometrical structure of both the stable and the unstable manifolds usally referred to as a homoclinic tangle. When a homoclinic tangle has developed, a trajfectory that comes close to the saddle point behaves in an erratic way, showing sensitivity to initial conditions.

We set up agent based models in which agents have low or zero cognitive ability. We examine two quite diverse socio-economic phenomena, namely the distribution of the cumulative size of economic recessions in the United States and the distribution of the number of crimes carried out by individuals. We show that the key macro-phenomena of the two systems can be shown to emerge from the behaviour of these agents. In other words, both the distribution of economic recessions and the distribution of the number of crimes can be accounted for by models in which agents have low or zero cognitive ability.