TOWARDS AN ALGORITHMIC REVOLUTION IN ECONOMIC THEORY

Abstract This is an attempt to tell a coherent story of a possible path towards an algorithmic revolution in economic theory, based on foundational debates in mathematics. First, by exposing the non‐computational content of classical mathematics, and its foundations, it is shown that both set theory and the tertium non datur can be dispensed with, as foundational concepts. Next, then, as a natural sequel, it follows that every kind of economic theory that bases its theoretical underpinning on classical mathematics can be freed from these foundations and can be made naturally algorithmic. This will make the subject face, in an all pervasive way, absolutely (algorithmically) undecidable decision problems. The thrust of the path towards an algorithmic revolution in economics lies, then, in pointing out that only a radically new mathematical vision of microeconomics, macroeconomics, behavioural economics, game theory, dynamical systems theory and probability theory can lead us towards making economic theory a meaningfully applied science and free of mysticism and subjectivism.     

Non-maximum Disequilibrium Macrodynamics

In his stimulating Nobel Prize Lecture, Paul Samuelson made the important point that there were interesting macrodynamic systems which could, in no sensible sense, be associated with maximization problems. The paradigmatic example he chose was the multiplier-accelerator system. In this paper I make an attempt to explore the connection between macrodynamics, rationality and computability against the backdrop provided by Samuelson's observation and Richard Goodwin's nonlinear methodological credo. It is shown that non-maximum, disequilibrium macrodynamics is perfectly consistent with standard rationality postulates.     

NON‐LINEAR DYNAMICS,COMPLEXITY AND RANDOMNESS: ALGORITHMIC FOUNDATIONS

Abstract In this paper I make an attempt to describe, discuss and extend a few aspects of the rich mathematical tapestry that can be woven with rigorous notions of non‐linear dynamics, complexity and randomness, in terms of algorithmic mathematics. It is a tapestry that I try to weave with economic analysis, economic theory and economic modelling in mind. All three notions – that is, non‐linear dynamics, complexity and randomness – have a rich conceptual, modelling or analytic tradition in core areas of economic theory, both at the micro and macro levels. It is the algorithmic foundation I try to provide for them that could be considered the novel contribution in this paper. Once the algorithmic foundations are in place, it is, for example, almost natural to consider the famed difficulties of obtaining closed form solutions for non‐linear, complex or random dynamic models in economics almost a trivial vestige of a pre‐simulation era in mathematical modelling.     

Path Dependence or Path Creation?

We discuss the assumptions that underlie path dependence, as defined by Vergne and Durand, and then provide the outlines of an alternative perspective which we label as path creation. Path creation entertains a notion of agency that is distributed and emergent through relational processes that constitute phenomena. Viewed from this perspective, ‘initial conditions’ are not given, ‘contingencies’ are emergent contexts for action, ‘self‐reinforcing mechanisms’ are strategically manipulated, and ‘lock‐in’ is but a temporary stabilization of paths in‐the‐making. We develop these points using a narrative approach and highlight the theoretical and methodological implications of our perspective.     

A disequilibrium macrodynamic model of fluctuations

A non-linear disequilibrium macrodynamic model of fluctuations in the labour and product markets, mediated by variations in factor shares, is developed and the existence of a periodic orbit is proved using the Hopf bifurcation theorem.     

VARIATIONS ON THE THEME OF CONNINGa IN MATHEMATICAL ECONOMICS

Abstract The mathematization of economics is almost exclusively in terms of the mathematics of real analysis which, in turn, is founded on set theory (and the axiom of choice) and orthodox mathematical logic. In this paper I try to point out that this kind of mathematization is replete with economic infelicities. The attempt to extract these infelicities is in terms of three main examples and one general discussion: dynamics, policy and rational expectations and learning are the examples; a game theory without ‘subjectivism’, based on the axiom of determinateness, is discussed in general terms. The focus is on the role and reliance of standard fixed‐point theorems in orthodox mathematical economics.     

Undecidability, Computation Universality and Minimality in Economic Dynamics*

An attempt is made, in this paper, to pose questions about economic dynamics in the broad areas of microeconomics, behavioural economics and macroeconomics from the point of view of classical recursion theory. This viewpoint makes it imperative that the fundamental economic entities in question are given an algorithmic formulation. Algorithms, in turn, are intrinsically dynamic objects which, if they are nontrivial, encapsulate nonlinear dynamics in novel ways such that it is possible to ask decidability questions and obtain effective answers about the economic entities.
It is shown, formally, that rational economic behaviour is comfortably consistent with nonmaximum, disequilibrium and unstable economic dynamics in core areas of microeconomics, behavioural economics and macroeconomics.