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Uncomputability and Undecidability in Economic Theory

K. Vela Velupillai ()

No 806, Department of Economics Working Papers from Department of Economics, University of Trento, Italia

Abstract: Economic theory, game theory and mathematical statistics have all increasingly become algorithmic sciences. Computable Economics, Algorithmic Game Theory ([28]) and Algorithmic Statistics ([13]) are frontier research subjects. All of them, each in its own way, are underpinned by (classical) recursion theory - and its applied branches, say computational complexity theory or algorithmic information theory - and, occasionally, proof theory. These research paradigms have posed new mathematical and metamathematical questions and, inadvertently, undermined the traditional mathematical foundations of economic theory. A concise, but partial, pathway into these new frontiers is the subject matter of this paper. Interpreting the core of mathematical economic theory to be defined by General Equilibrium Theory and Game Theory, a general - but concise - analysis of the computable and decidable content of the implications of these two areas are discussed. Issues at the frontiers of macroeconomics, now dominated by Recursive Macroeconomic Theory, are also tackled, albeit ultra briefly. The point of view adopted is that of classical recursion theory and varieties of constructive mathematics.

Keywords: General Equilibrium Theory; Game Theory; Recursive Macro-economics; (Un)computability; (Un)decidability; Constructivity (search for similar items in EconPapers)
JEL-codes: C60 C63 C68 C70 C79 (search for similar items in EconPapers)
Date: 2008
New Economics Papers: this item is included in nep-hpe
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