Computable Economics: The Arne Ryde Memorial Lectures

Computable Economics: The Arne Ryde Memorial Lectures

Computable Economics: The Arne Ryde Memorial Lectures

Computable Economics: The Arne Ryde Memorial Lectures

Synopsis

In the field of economic analysis, computability in the formation of economic hypotheses is seen as the way forward. In this book, Professor Velupillai implements a theoretical research program along these lines. Choice theory, learning rational expectations equlibria, the persistence ofadaptive behaviour, arithmetical games, aspects of production theory, and economic dynamics are given recursion theoretic (i.e. computable) interpretations. These interpretations lead to new kinds of questions being posed by the economic theorist. In particular, recurison theoretic decision problemsreplace standard optimisation paradigms in economic analysis. Economic theoretic questions, posed recursion-theoretically, lead to answers that are ambiguous: undecidable choices, uncomputable learning processes, and algorithmically unplayable games become standard answers. Professor Velupillaiargues that a recursion theoretic formalisation of economic analysisComputable Economicsmakes the subject intrinsically inductive and computational.

Excerpt

What must be achieved is in fact this: That every paralogism be recognized as an error of calculation, and that every sophism when expressed in this new kind of notation . . . be corrected easily by the laws of this philosophic grammar. . . . Once this is done, then when a controversy arises, disputation will no more be needed between two philosophers than between two computers. It will suffice that, pen in hand, they sit down . . . and say to each other: Let us calculate.

Leibniz (1686/1965 : xiv; final emphasis added).

2.1 Introduction

I do think there are some very worthwhile and interesting analogies between complexity issues in computer science and in economics. For example, economics traditionally assumes that the agents within an economy have universal computing power . . . Computer scientists deny that an algorithm can have infinite computing power.

Karp (1987 : 464)

I have tried, in the opening paragraphs of the previous chapter, to delineate the nature of computable economics by suggesting that recursion-theoretic formalisms of economic fundamentals, broadly conceived, are the key features of the subject. This does not, of course, restrict the scope of computable economics to the “pure” aspects of recursion theory. the “applied” wings of recursion theory, in particular the varieties of complexity theories — computational, algorithmic, stochastic, and diophantine — have an equally important role to play in redirecting the formalization of economic fundamentals. By this I mean a redirection away from the dominant set-theoretic and model-theoretic formalisms of economic fundamentals. the hope is that the

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