Computability Theory in Economics - Frontiers and a Restrospective
This is an outline of the origins and development of the way computability theory was incorporated into formal economic theory. I try to place in the context of the development of computable economics, some of the classics of the subject as well as those that have, from time to time, been credited with having contributed to the advancement of the field. Speculative methodological thoughts and reflections suggest directions in which fruitful research could proceed to reduce the current deficit in the epistemology of computation in economics. Finally, thoughts on where the frontiers of computable economics are, and how to move towards them, conclude the paper. In a precise sense -- both historically and analytically -- it would not be an exaggeration to claim that both the origins of computable economics and its frontiers are defined by two classics, both by Banach and Mazur: that one page masterpiece by Banach and Mazur and the unpublished Mazur conjecture of 1928, and its unpublished proof by Banach. For the undisputed original classic of computable economics is Rabin's effectivization of the Gale-Stewart game; the frontiers, as I see them, are defined by recursive analysis and constructive mathematics, underpinning computability over the computable and constructive reals and providing computable foundations for the economist's Marshallian penchant for curve-sketching and, in general, the contents of Theoretical Computer Science, Vol. 219, Issue 1-2). The former work has its roots in the Banach-Mazur game, at least in one reading of it; the latter in Banach and Mazur (1937), as well as other, earlier, contributions, not least by Brouwer.
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