Computability in Europe 2006
Logical Approaches to Computational Barriers
|Slot:||Tue, 14:50-15:10, Faraday J (col. 5)|
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. References: 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, January 2004. 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||
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