test FOO test
Computability in Europe 2006
Logical Approaches to Computational Barriers
The lack of effective procedures to determine winning strategies
cleverly identified by Brian Arthur (1994) in an informal statement
of this problem in a stock market game called the Minority or
El Farol game results in the adoption of a multiplicity of meta-models
for forecasting and strategizing by agents. The presence of contrarian
payoff structures or hostile agents in a game theoretic framework are
shown to result in the fundamental non-computable fixed point that
corresponds to Gödel's undecidable proposition. Any best response
function of the game which is constrained to be a total computable
function then represents the productive function of the Emil Post
(1944) set theoretic proof of the Gödel Incompleteness result. The
productive function implements strategic innovation and objects of
novelty or 'surprise' result in undecidable structure changing
dynamics in the system. Oppositional or contrarian structures,
self-reflexive calculations and the necessity to innovate to out-smart
hostile agents are ubiquitous in economic systems. However, as first
noted in Binmore (1987) and Spear (1987), extant game theory and
economic theory cannot model the strategic and logical necessity of
Gödelian indeterminism in economic systems. This paper reports on
some formal results developed in Markose (2002, 2004, 2005) on the
implications of the Gödelian incompleteness result for economics.
Keywords: Effective procedures; self-reflexivity; contrarian payoff
structures; strategic innovation; Gödel Incompleteness.
Arthur, W.B., (1994). 'Inductive Behaviour and Bounded Rationality',
American Economic Review, 84, pp.406-411.
Binmore, K. (1987), 'Modelling Rational Players: Part 1',
Journal of Economics and Philosophy, vol. 3, pp. 179-214.
Markose, S.M, 2005 , 'Computability and Evolutionary Complexity :
Markets as Complex Adaptive Systems (CAS)', Economic Journal ,
vol. 115, pp.F159-F192.
Markose, S.M, 2004, 'Novelty in Complex Adaptive Systems (CAS):
A Computational Theory of Actor Innovation', Physica A: Statistical
Mechanics and Its Applications, vol. 344, pp. 41- 49. Fuller details
in University of Essex, Economics Dept. Discussion Paper No. 575,
Markose, S.M., July 2002, 'The New Evolutionary Computational
Paradigm of Complex Adaptive Systems: Challenges and Prospects For
Economics and Finance', In, Genetic Algorithms and Genetic
Programming in Computational Finance, Edited by Shu-Heng Chen, Kluwer
Academic Publishers, pp.443-484 . Also Essex University Economics
Department DP no. 552, July 2001.
Post, E.(1944). 'Recursively Enumerable Sets of Positive Integers
and Their Decision Problems', Bulletin of American Mathematical
Society, vol.50, pp.284-316.
Spear, S.(1989), 'Learning Rational Expectations Under Computability
Constraints', Econometrica , vol.57, pp.889-910.
websites: Arnold Beckmann