Computable Foundations for Economics is a unified collection of
essays, some of which are published here for the first time and all
of which have been updated for this book, on an approach to
economic theory from the point of view of algorithmic mathematics.
By algorithmic mathematics the author means computability theory
and constructive mathematics. This is in contrast to orthodox
mathematical economics and game theory, which are formalised with
the mathematics of real analysis, underpinned by what is called the
ZFC formalism, i.e., set theory with the axiom of choice. This
reliance on ordinary real analysis and the ZFC system makes
economic theory in its current mathematical mode completely
non-algorithmic, which means it is numerically meaningless.
The book provides a systematic attempt to dissect and expose the
non-algorithmic content of orthodox mathematical economics and game
theory and suggests a reformalization on the basis of a strictly
rigorous algorithmic mathematics. This removes the current
schizophrenia in mathematical economics and game theory, where
theory is entirely divorced from algorithmic applicability - for
experimental and computational exercises.
The chapters demonstrate the uncomputability and
non-constructivity of core areas of general equilibrium theory,
game theory and recursive macroeconomics. The book also provides a
fresh look at the kind of behavioural economics that lies behind
Herbert Simon's work, and resurrects a role for the noble classical
traditions of induction and verification, viewed and formalised,
now, algorithmically. It will therefore be of particular interest
to postgraduate students and researchers in algorithmic economics,
game theory and classical behavioural economics.
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