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.
Part I: Foundations
1. The Incomputable, the Nonconstructive and the
Undecidable in Mathematical Economics
2. Advanced Computational Complexity
Theory from an Elementary Standpoint
3. Economic Dynamics and Computation
Recursion Theoretic Foundations for the Icarus Tradition 4: Lets Take the
Con out of Mathematical Economics Part II: General Equilibrium Theory
5.
Effectivity and Constructivity in Economic Theory
6. Algorithmic Foundations
of Computable General Equilibrium Theory
7. Uncomputability and
Undecidability in Economic Theory Part III: Methodology
8. The Unreasonable
Ineffectivity of Mathematics in Economics
9. A Constructive Interpretation of
Sraffas Mathematical Economics
10. The Computable Alternative in the
Mathematization of Economics Part IV: Simons Behavioural Economics A
Computable Vision
11. Computable Rationality
12. Boundedly Rational Choice
and Satisficing Decisions
13. Simons Epicurean Adventures A Prolegomena.
Appendix 1 to Part IV: Artificing a Rationally Unbounded Life. Appendix 2 to
Part IV: The Logic of Discovery, Problem Solving and Retroduction. Appendix 3
to Part IV: Herbert Simons Letter on Computable Economics Part V: Inductive
Reflections
14. De-Mystifying Induction, Falsification and other Popperian
Extravaganzas
15. Re-reading Jevonss Principles of Science: Induction Redux
16. Impossibility of Effectively Computable Inductive Policies in a Complex
Dynamic Economy. Part VI: Concluding Notes
17. Epilogue A Research Program
for the Algorithmic Social Sciences
Vela Velupillai is a Professor of Economics, both in the faculty of economics and in its graduate school, CIFREM, at the University of Trento, Italy. He is also a Senior Visiting Professor at the Madras School of Economics.
