Computable economics. The Arne Ryde memorial lectures (Q2782588)

This is an essay-like monograph proposing a recursion theoretic formalization of economic analysis, called by the author \textit{Computable economics}. In the introductory chapter he writes that the relevant research program can be realized (p. 14, l. 5b, to p. 16, l. 7a) ``\dots{} in one of two ways (or in an eclectic combination of the two): eitherNEWLINENEWLINENEWLINE(a) seek or investigate the economic implications of recursion-theoretic restrictions to the standard primitive concepts of economic analysis; orNEWLINENEWLINENEWLINE(b) go back to one of the nodes of the decision-tree that characterizes the development of the mathematization of economics (cf. Leijonhufvud 1991); e.g. to the nodes at which existence, uniqueness and stability questions were rigorously posed and reconsidered for general economic equilibrium; then try to answer the question recursion-theoretically, rather than set-theoretically or model-theoretically''. Then he declares: ``My own inclination is to go the latter way (i.e. (b)), although my limited knowledge and abilities force me to go the former way (i.e. (a)). As a result of these conflicting features, this work is mildly eclectic, dominated by the former method with a few infusions along the latter path.'' NEWLINENEWLINENEWLINEThe book consists of 10 chapters and an Appendix. The list of references contains about 200 items. The contents of the book is the following: NEWLINENEWLINENEWLINE1) Introduction and Overview; 2) Ideas, Pioneers and Precursors; 3) Computable Rationality; 4) Adaptive behaviour; 5) The Modern Theory of Induction; 6) Learning in a Computable Setting; 7) Effective Playability in Arithmetical Games; 8) Notes on Computational Complexity; 9) Explorations in Computable Economics; 10) Conclusions: Reflections and Hopes; Appendix: A Child's Guide to Elementary Aspects of Computability Theory; References; Author Index; Subject Index. NEWLINENEWLINENEWLINEIn Chapter 2 the author names the pioneers and precursors of computable economics: ``Rabin (games) [1957], Lewis (games, rationality, equilibria), Spear (learning), and Rustem and Velupillai (rationality) [1990]''. The discussion, summaries and generalizations of their works are found in Chapters 3, 6, 7 and 9. The historical background is well documented and accurately presented. NEWLINENEWLINENEWLINENEWLINENEWLINENEWLINEMathematics is found in the book, first of all, in the Appendix [from Turing machine computable functions to enumerability and recursive functions and sets]. More mathematics is present also in the Sections: 3.2 The rational economic agent as a Turing machine and 3.3 The nonefectivity of preference generation [choice functions, computability, decidability]; 4.3 A computable basis for the study of trial-and-error processes in rational choice [neural nets]; 5.2 The modern theory of induction and 5.3 Gold's learning and Solomonoff's inductive inference [Bayes' formula exploited]; 6.3 Computable analytic underpinning for the Spear model [functional dynamic equation whose solution can be identified as the rational expectation equilibrium and learned recursively]; 7.3 Rabin's computable game - and extensions [nonexistence of a winning strategy]; 7.4 Arithmetical games [they are determined]; 8.3 Khachian's ellipsoid algorithm and the complexity of the policy design [an algorithm for linear programming terminating in polynomial time]. One also finds remarks on: Hahn-Banach theorem, Hilbert's tenth problem, William of Occam's razor, dynamical systems. NEWLINENEWLINENEWLINEIn the book there are over 160 footnotes. Each chapter and section begins with a motto (or two, altogether almost 50 quotes). After chapter headings we find quotes taken among others from Solow 1954, Rabin 1957, Leibniz 1686/1965, Wittgenstein 1980, Kemeny 1953, Simon 1969, Babbage 1864/1961, Bronowski 1978. Also in the text there is a lot of quotations from references. NEWLINENEWLINENEWLINEThe book under review is rich in ideas and problems and may inspire research work of specialists in mathematical economics.