Computability in Europe 2006
Logical Approaches to Computational Barriers

Regular Talk:
Gödelian Foundations of Non-Computability and Heterogeneity In Economic Forecasting and Strategic Innovation

Speaker: Sheri Markose
Slot: Array, 14:50-15:10, 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. 

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 2006-05-12