The impossibility of an effective theory of policy in a complex economy

theory of policy,dynamical system,computation universality,recursive rule,complex economy

Kolmogorov complexity and computably enumerable sets

We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing research on this topic, along with recent developments and open problems. Besides this survey, our main original result is the following characterization of the computably enumerable sets with trivial initial segment prefix-free complexity. A computably enumerable set $A$ is $K$-trivial if and only if the family of sets with complexity bounded by the complexity of $A$ is uniformly computable from the halting problem

Computation in Economics

This is an attempt at a succinct survey, from methodological and epistemological perspectives, of the burgeoning, apparently unstructured, field of what is often – misleadingly – referred to as computational economics. We identify and characterise four frontier research fields, encompassing both micro and macro aspects of economic theory, where machine computation play crucial roles in formal modelling exercises: algorithmic behavioural economics, computable general equilibrium theory, agent based computational economics and computable economics. In some senses these four research frontiers raise, without resolving, many interesting methodological and epistemological issues in economic theorising in (alternative) mathematical modesClassical Behavioural Economics, Computable General Equilibrium theory, Agent Based Economics, Computable Economics, Computability, Constructivity, Numerical Analysis

Tabular degrees in \Ga-recursion theory

AbstractBailey, C. and R. Downey, Tabular degrees in \Ga-recursion theory, Annals of Pure and Applied Logic 55 (1992) 205–236.We introduce several generalizations of the truth-table and weak-truth-table reducibilities to \Ga-recursion theory. A number of examples are given of theorems that lift from \Gw-recursion theory, and of theorems that do not. In particular it is shown that the regular sets theorem fails and that not all natural generalizations of wtt are the same

Computational phenotypes : where the theory of computation meets evo-devo

This article argues that the Chomsky Hierarchy can be reinterpreted as a developmental morphospace constraining the evolution of a discrete and finite series of computational phenotypes. In doing so, the theory of Morphological Evolution as stated by Pere Alberch, a pioneering figure of Evo-Devo thinking, is adhered to

Computational Depth and Reducibility

This paper investigates Bennett\u27s notions of strong and weak computational depth (also called logical depth) for infinite binary sequences. Roughly, an infinite binary sequence x is defined to be weakly useful if every element of a non-negligible set of decidable sequences is reducible to x in recursively bounded time. It is shown that every weakly useful sequence is strongly deep. This result (which generalizes Bennett\u27s observation that the halting problem is strongly deep) implies that every high Turing degree contains strongly deep sequences. It is also shown that, in the sense of Baire category, almost every infinite binary sequence is weakly deep, but not strongly deep

Norms as Emergent Properties of Adaptive Learning: The Case of Economic Routines

Strategic interaction among autonomous decision-makers is usually modelled in economics in game-theoretic terms or within the framework of General Equilibrium. Game-theoretic and General Equilibrium models deal almost exclusively with the existence of equilibria and do not analyse the processes which might lead to them. Even when existence proofs can be given, two questions are still open. The first concerns the possibility of multiple equilibria, which game theory has shown to be the case even in very simple models and which makes the outcome of interaction unpredictable. The second relates to the computability and complexity of the decision procedures which agents should adopt and questions the possibility of reaching an equilibrium by means of an algorithmically implementable strategy. Some theorems have recently proved that in many economically relevant problems equilibria are not computable. A different approach to the problem of strategic interaction is a "constructivist" one. Such a perspective, instead of being based upon an axiomatic view of human behaviour grounded on the principle of optimisation, focuses on algorithmically implementable "satisfycing" decision procedures. Once the axiomatic approach has been abandoned, decision procedures cannot be deduced from rationality assumptions, but must be the evolving outcome of a process of learning and adaptation to the particular environment in which the decision must be made. This paper considers one of the most recently proposed adaptive learning models: Genetic Programming and applies it to one the mostly studied and still controversial economic interaction environment, that of oligopolistic markets. Genetic Programming evolves decision procedures, represented by elements in the space of functions, balancing the exploitation of knowledge previously obtained with the search of more productive procedures. The results obtained are consistent with the evidence from the observation of the behaviour of real economic agents