文档介绍：All That I Have to Say Has Already Crossed Your Mind *We thank Duncan K. Foley, Young Back Choi, Richard Langlois, Larry Samuelson, Kumaraswamy Velupillai, and an anonymous referee for ments, and Yaw Nyarko for providing research materials. Any limits or errors of analysis are our own.
[Metroeconomica, ing]
Roger Koppl
Department of Economics and Finance
Fairleigh Dickinson University
Madison, NJ 07940 USA
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J. Barkley Rosser, Jr.
Department of Economics
James Madison University
Harrisonburg, VA USA
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February 2002
ABSTRACT
We present three arguments regarding the limits to rationality, prediction, and control in economics, based on Morgenstern's analysis of the Holmes-Moriarty problem. The first uses a standard metamathematical theorem putability to indicate logical limits to forecasting the future. The second provides possible nonconvergence for Bayesian forecasting in infinite dimensional space. The third shows the impossibility of puter perfectly forecasting an economy with agents knowing its forecasting program. Thus, economic order is partly the product of something other than calculative rationality. The joint presentation of these existing results should introduce the reader to implications of these concepts for certain shared concerns of Keynes and Hayek.
“All that I have to say has already crossed your mind,” said he.
“Then possibly my answer has crossed yours,” I replied.
“You stand fast?”
“Absolutely.”
The Final Problem
I. Introduction
Self-reference arises naturally in economics. Augustin Cournot (1838) presented a model of duopoly in which each party must form conjectures about the actions of the other party. Implicitly, this means that each player is forming conjectures about the conjectures of the other player. I think that you think that I think. Herbert Simon called the problem Cournot raised “the permanent and ineradicable scandal of economic theory”(1976, p. 140). The “reflexivity” of such situ