There is indeed a rather large literature on this in game theory and other areas, with many of the issues unresolved. Indeed, a central battle between Robert Aumann and Ken Binmore involves this issue. The Albin/Foley volume is quite good on this. I would note that in terms of computability the most common problem is that of the halting problem. It has long been known that Godelian problems can generate halting problems, darned system just won't stop and spit out an answer.
Some have argued that it is the problem of self-referencing that is at issue here. This was a theme of the popular volume by Douglas Hofstadter, _Godel, Escher, Bach_. Certainly this becomes a problem in game theory as one starts to allow full consideration of all possible outcomes. The specific issue between Aumann and Binmore involves the backward-induction problem that has implications for financial markets.
A few references beyond Albin/Foley and Hofstadter include: general on infinite self-referencing with a lot of other references: John Conlisk, "Why Bounded Rationality?" _Journal of Economic Literature, June 1996, vol. 34, no. 2, pp. 669-700. Binmore's main argument regarding Godelian implications for game theory is Ken Binmore, "Modeling Rational Players I," _Economics and Philosophy_, 1987, vol. 3, pp. 9-55.
His debate with Aumann can be seen in Robert Aumann, "Backward Induction and Common Knowledge of Rationality," Games and Economic Behavior, 1995, vol. 8, pp. 6-19. Ken Binmore, "Rationality and Backward Induction," _Journal of Economic Methodology_, 1997, vol. 4, pp. 23-44.
A classic reference is R.J. Solomonoff, "A Formal Theory of Inductive Inference," Parts I and II, _Information and Control_, 1964, vol. 7, pp. 1-22 and 224-254.
Some other references on the infinite regress problem include B.L. Lipman, "How to Decide How to Decide How to...: Modeling Limited Rationality," _Econometrica_, 1991, vol. 59, pp. 1105-1125. L.G. Epstein and T. Wang, "Beliefs About Beliefs Without Probabilities," _Econometrica_, 1996, vol. 64, pp. 1343-1373.
A recent more advanced book dealing with the computability issue, per se is L. Blum, F. Cucker, M. Shub, and S. Smale, _Complexity and Real Computation_, 1998, New York: Springer-Verlag.
Also, I have a paper with Roger Koppl dealing with various aspects of this issue, entitled, "Everything I Might Say Will Already Have Passed Through Your Mind." The latest version, just resubmitted to a journal after revision, is available on my website at http://cob.jmu.edu/rosserjb Barkley Rosser -----Original Message----- From: Lisa & Ian Murray <seamus at accessone.com> To: lbo-talk at lists.panix.com <lbo-talk at lists.panix.com> Date: Wednesday, May 24, 2000 7:04 PM Subject: RE: Godel and economics?
> accept that Godel's results have implications for
> economics,
>
> >Ian
>
> OK, I'll bite. What are these?
>
> cheers
>
> dd
>==========
>That would take a book that has yet to be written. I'll just give you a
>couple of quotes from Duncan Foley's intro to Albin's "Barriers and Bounds
>to Rationality and then a link or two. IMHO free trade is a 90 pound theory
>trying to solve a 20 ton problem.
>
>"A fundamental question about any problem is whether there exists a
>computational procedure for solving it that will eventually come up with an
>answer...Problems of this type are decidable. One of the central
>mathematical discoveries of the century is that undecidable problems
exist."
>
>"The theory of computability and computational complexity suggests that
>there are two inherent limitations to the rational choice paradigm. One
>limitation stems from the possibility that the agent's problem is in fact
>undecidable so that no computational procedure exists which for all inputs
>will give her the needed answer in a finite time. A second limitation is
>posed by computational complexity in that even if her problem is decidable,
>the computational cost of solving it may in many situations be so large as
>to overwhelm any possible gains from the optimal choice of action."
>
>"Most human beings can work out the dynamics of a two or three state
system,
>but few can carry on chains of recursion of even ten periods, not to speak
>of the hundreds of thousands that easily arise in complex financial
>transactions or complex diplomatic or military confrontations. Even
periodic
>systems, if they involve a large number of degrees of freedom, can
challenge
>the computational resources built into our brains by evolution."
>
>The best quote comes from Albin himself though: "An economic system is
shown
>on its own terms to be as rich as general mathematics and the analogy
>suggests the impossiblity of proposing nonvacuous universal properties for
>its functions. The assertion of such properties is HUBRIS" [emphasis his].
>
>To the extent that Brad and others suggest game-theoretic disourse ino
their
>attempts to explain and justify free trade, they cannot avoid Godel's
>results when they attempt a formal explication of the terms and decision
>procedures that would bring such an economic prescription to the trading
>nations of the world. To say that free trade is the optimum policy for
>dealing with international economic relations is tantamount to a prediction
>that leaves out more factors driving economic history than it admits; for
>that reason alone it is problematic, especially in light of attempts to
>explicate and predict/simulate possible economic policy outcomes using game
>theory with computable general equilibrium models.
>
>http://www.wcl.american.edu/pub/faculty/boyle/ipmat.htm
>
>http://www.sunysb.edu/philosophy/faculty/pgrim/SPATIALP.HTM
>
>Also try "Games, Information and Politics" by Scott Gates and Brian D.
Humes
>which has some extremely interesting chapters Conybeare's classic "Trade
>Wars" and Adam Przeworski's "Democracy and the Market"
>
>Ian
>
>
>
>
>
>
>
>