Learning in evolutionary environments

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Learning in Evolutionary Environments

The purpose of this work is to present a sort of short selective guide to an enormous and diverse literature on learning processes in economics. We argue that learning is an ubiquitous characteristic of most economic and social systems but it acquires even greater importance in explicitly evolutionary environments where: a) heterogeneous agents systematically display various forms of "bounded rationality"; b) there is a persistent appearance of novelties, both as exogenous shocks and as the result of technological, behavioural and organisational innovations by the agents themselves; c) markets (and other interaction arrangements) perform as selection mechanisms; d) aggregate regularities are primarily emergent properties stemming from out-of-equilibrium interactions. We present, by means of examples, the most important classes of learning models, trying to show their links and differences, and setting them against a sort of ideal framework of "what one would like to understand about learning...". We put a signifiphasis on learning models in their bare-bone formal structure, but we also refer to the (generally richer) non-formal theorising about the same objects. This allows us to provide an easier mapping of a wide and largely unexplored research agenda.Learning, Evolutionary Environments, Economic Theory, Rationality

Geometric Interpretation of Chaos in Two-Dimensional Hamiltonian Systems

Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit segments evolved in 2-D potentials, examining how various orbital properties correlate with the mean value and dispersion, and k, of the trace K of the curvature. Unlike most analyses, which have attributed chaos to negative curvature, this work exploits the fact that geodesics can be chaotic even if K is everywhere positive, chaos arising as a parameteric instability triggered by regular variations in K along the orbit. For ensembles of fixed energy, with both regular and chaotic segments, simple patterns connect the values of and k for different segments, both with each other and with the short time Lyapunov exponent X. Often, but not always, there is a near one-to- one correlation between and k, a plot of these quantities approximating a simple curve. X varies smoothly along this curve, chaotic segments located furthest from the regular regions tending systematically to have the largest X's. For regular orbits, and k also vary smoothly with ``distance'' from the chaotic phase space regions, as probed, e.g., by the location of the initial condition on a surface of section. Many of these observed properties can be understood qualitatively in terms of a one-dimensional Mathieu equation.Comment: 16 pages plus 9 figures, LaTeX, no macros required to appear in Physical Review

On the mean/variance relationship of the firm size distribution: evidence and some theory

In this paper we make use of firm-level data for a sample of European countries to prove the existence of a positive linear relationship between the mean and the variance of firms’ size, an empirical regularity known in mathematical biology as the Taylor power law. A computerized experiment is used to show that the estimated slope of the linear relationship can be fruitfully employed to discriminate among alternative theories of firms’ growth.Taylor power law; Firm size distribution; Stochastic growth

Simulation models of technological innovation: A Review

The use of simulation modelling techniques in studies of technological innovation dates back to Nelson and Winter''s 1982 book "An Evolutionary Theory of Economic Change" and is an area which has been steadily expanding ever since. Four main issues are identified in reviewing the key contributions that have been made to this burgeoning literature. Firstly, a key driver in the construction of computer simulations has been the desire to develop more complicated theoretical models capable of dealing with the complex phenomena characteristic of technological innovation. Secondly, no single model captures all of the dimensions and stylised facts of innovative learning. Indeed this paper argues that one can usefully distinguish between the various contributions according to the particular dimensions of the learning process which they explore. To this end the paper develops a taxonomy which usefully distinguishes between these dimensions and also clarifies the quite different perspectives underpinning the contributions made by mainstream economists and non-mainstream, neo-Schumpeterian economists. This brings us to a third point highlighted in the paper. The character of simulation models which are developed are heavily influenced by the generic research questions of these different schools of thought. Finally, attention is drawn to an important distinction between the process of learning and adaptation within a static environment, and dynamic environments in which the introduction of new artefacts and patterns of behaviour change the selective pressure faced by agents. We show that modellers choosing to explore one or other of these settings reveal their quite different conceptual understandings of "technological innovation".economics of technology ;

The multi-fractal structure of contrast changes in natural images: from sharp edges to textures

We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a decomposition of pixels of the image in sets, the fractal components of the image, such that each set only contains points characterized by a fixed stregth of the singularity of the contrast gradient in its neighborhood. A crucial role in this description of images is played by the behavior of contrast differences under changes in scale. Contrary to naive scaling ideas where the image is thought to have uniform transformation properties \cite{Fie87}, each of these fractal components has its own transformation law and scaling exponents. A conjecture on their biological relevance is also given.Comment: 41 pages, 8 figures, LaTe

Economics, realism and reality: a comparison of Mäki and Lawson

There is presently considerable debate about the application and interpretation of realism in economics. Interest in this area of the philosophy and methodology of economics has intensified over the last twenty years, especially due to the substantial contributions by Uskali Mäki and Tony Lawson respectively. Although their work falls under the same banner of realism in economics, their projects differ significantly in many important respects. This review tries to clarify the contrasting approaches of each author and explains the main reasons for the differences between them. The emphasis is on clarification of their respective positions rather than a comprehensive critical evaluation as such.