Edited by K. Vela Velupillai, Professor of Economics, University of Trento, Italy, Stefano Zambelli, Professor of Economics, University of Trento, Italy and Stephen Kinsella, Lecturer in Economics, University of Limerick, Ireland

• Contents:Acknowledgements Introduction K. Vela Velupillai, Stephen Kinsella and Stefano Zambelli PART I FOUNDATIONS OF COMPUTABLE ECONOMICS 1. Stephen C. Kleene (1981), ‘Origins of Recursive Function Theory’2. A.M. Turing (1954), ‘Solvable and Unsolvable Problems’ PART II MATHEMATICAL AND METHODOLOGICAL FOUNDATIONS OF COMPUTABLE ECONOMICS 3. L.E.J. Brouwer (1952), ‘An Intuitionist Correction of the Fixed-Point Theorem on the Sphere’4. Allen Newell, J.C. Shaw and Herbert A. Simon (1958), ‘Elements of a Theory of Human Problem Solving’5. Ronald Harrop (1961), ‘On The Recursivity of Finite Sets’ 6. H. Steinhaus (1965), ‘Games, An Informal Talk’7. Hilary Putnam ([1967] 1975), ‘The Mental Life of Some Machines’8. Douglas S. Bridges (1999), ‘Constructive Methods in Mathematical Economics’PART III CLASSICS OF COMPUTABLE CHOICE THEORY 9. Douglas S. Bridges (1982), ‘Preference and Utility: A Constructive Development’10. Alain A. Lewis (1985), ‘On Effectively Computable Realizations of Choice Functions’11. Alain A. Lewis (1985), ‘The Minimum Degree of Recursively Representable Choice Functions’12. Berc Rustem and Kumaraswamy Velupillai (1990), ‘Rationality, Computability, and Complexity’13. Gregory Lilly (1993), ‘Recursiveness and Preference Orderings’ PART IV COMPUTABLE GAME THEORY 14. Michael O. Rabin (1957), ‘Effective Computability of Winning Strategies’15. Luca Anderlini (1990), ‘Some Notes on Church’s Thesis and the Theory of Games’16. Kislaya Prasad (1991), ‘Computability and Randomness of Nash Equilibrium in Infinite Games’17. David Canning (1992), ‘Rationality, Computability, and Nash Equilibrium’18. Kislaya Prasad (1997), ‘On the Computability of Nash Equilibria’19. K. (Vela) Velupillai (1997), ‘Expository Notes on Computability and Complexity in (Arithmetical) Games’20. Marcelo Tsuji, Newton C.A. Da Costa and Francisco A. Doria (1998), ‘The Incompleteness of Theories of Games’ PART V COMPUTABLE GENERAL EQUILIBRIUM THEORY 21. Rolf Ricardo Mantel (1968), ‘Toward a Constructive Proof of the Existence of Equilibrium in a Competitive Economy’22. Hirofumi Uzawa (1962), ‘Walras’ Existence Theorem and Brouwer’s Fixed-Point Theorem’23. Herbert E. Scarf (1984), ‘The Computation of Equilibrium Prices’24. K. Vela Velupillai (2006), ‘Algorithmic Foundations of Computable General Equilibrium Theory’25. Yasuhito Tanaka (2008), ‘Undecidability of Uzawa Equivalence Theorem and LLPO (Lesser Limited Principle of Omniscience)’ PART VI COMPUTABLE MACROECONOMICS 26. Stephen E. Spear (1989), ‘Learning Rational Expectations Under Computability Constraints’27. Francesco Luna (1997), ‘Learning in a Computable Setting. Applications of Gold’s Inductive Inference Model’28. Stefano Zambelli (2004), ‘Production of Ideas by Means of Ideas: A Turing Machine Metaphor’29. K. Vela Velupillai (2007), ‘The Impossibility of an Effective Theory of Policy in a Complex Economy’PART VII COMPUTABLE MICROECONOMICS 30. Alain A. Lewis (1991), ‘On the Effective Content of Asymptotic Verifications of Edgeworth’s Conjecture’31. Marcel K. Richter and Kam-Chau Wong (1999), ‘Non-Computability of Competitive Equilibrium’32. K. Vela Velupillai (2009), ‘Uncomputability and Undecidability in Economic Theory’ PART VIII COMPUTABLE AND SOCIAL CHOICE THEORY 33. Alain A. Lewis (1988), ‘An Infinite Version of Arrow’s Theorem in the Effective Setting’34. Jerry S. Kelly (1988), ‘Social Choice and Computational Complexity’35. H. Reiju Mihara (1997), ‘Arrow’s Theorem and Turing Computability’ PART IX EXOTICA 36. A.R.D. Mathias (1992), ‘The Ignorance of Bourbaki’37. Luca Anderlini and Leonardo Felli (1994), ‘Incomplete Written Contracts: Undescribable States of Nature’38. K. Vela Velupillai (2005), ‘The Unreasonable Ineffectiveness of Mathematics in Economics’