Evolutionary Foundations of Economic Science pp 161-194 | Cite as

# The Complexities Generated by the Movement of the Market Economy

## Abstract

In previous chapters we have seen the advent of a new society, with the growing complexity of the market and technological innovations. We demonstrated the move away from the Gaussian world towards that of heavy tail distribution. To fully understand the latter distribution, we need to recognize a generalized central limit theorem, where the Gaussian distribution is simply a special case. We are therefore able to investigate several stable distributions and expand our idea of price equilibrium as a stable distribution. We will also discuss the central issue of how the market economy can generate complex dynamics. We use the trader dynamics system designed by Philip Maymin, and recreate his simulation dynamics for an automaton. This explicitly takes into account traders’ decisions in combined multiple layers: actions, mind states, memories of the trader and the market. These factors are normally regarded as influential components that govern price movements. In financial transactions, we dispense with psychological effects at individual and aggregate levels. These may no longer be secondary effects.

## Keywords

Central Limit Theorem Turing Machine Pareto Distribution Stable Distribution Heavy Tail Distribution## References

- Champernowne DG (1953) A model of income distribution. Econ J 63(2):318–351CrossRefGoogle Scholar
- Cook JD (2010) Central limit theorems. http://www.johndcook.com/central_limit_theorems.html, linked from Cook (2010): How the central limit theorem began? http://www.johndcook.com/blog/2010/01/05/how-the-central-limit-theorem-began/
- Fama E (1965) The behavior of stock market prices. J Bus 38:34–105. doi: 10.1086/294743 CrossRefGoogle Scholar
- Fama E (1970) Efficient capital markets: a review of theory and empirical work. J Finance 25(2):383–417. doi: 10.2307/2325486.JSTOR2325486 CrossRefGoogle Scholar
- Fisk PR (1961) The graduation of income distributions. Econometrica 29(2):171–185CrossRefGoogle Scholar
- Hawkins R (2011) Lending sociodynamics and economic instability. Physica A 390:4355–4369CrossRefGoogle Scholar
- Johnson NF, Jefferies P, Hui PM (2003) Financial market complexity: what physics can tell us about market behaviour. Oxford University Press, OxfordCrossRefGoogle Scholar
- Lévy P (1925) Calcul des probabilités. Gauthier-Villars, ParisGoogle Scholar
- Lux T (2009) Rational forecast or social opinion dynamics? Identification of interaction effects in a business climate survey. J Econ Behav Organ 72:638–655CrossRefGoogle Scholar
- Mainzer K (2007) Der kreative Zufall: Wie das Neue in die Welt kommt. C. H. Beck, MünchenGoogle Scholar
- Mandelbrot B (1963) The variation of certain speculative prices. J Bus 36(4):394–419. http://www.jstor.org/stable/2350970
- Manderbrot B (2001) Scaling in financial prices. Quant Finance 1(1):113–123CrossRefGoogle Scholar
- Mantegna RH, Stanley HE (2000) An introduction to econophysics: correlations and complexity in finance, Cambridge University Press, Cambridge, UKGoogle Scholar
- Maymin PZ (2007a) The minimal model of the complexity of financial security prices. Available through the Wolfram Demonstrations Project at http://demonstrations.wolfram.com/TheMinimalModelOfTheComplexityOfFinancialSecurityPrices/
- Maymin PZ (2007b) Minimal model of simulating prices of financial securities using an iterated finite automaton. Available through the Wolfram Demonstrations Project at http://demonstrations.wolfram.com/MinimalModelOfSimulatingPricesOfFinancialSecuritiesUsingAnIt/
- Maymin PZ (2007c) Exploring minimal models of the complexity of security prices. Available through the Wolfram Demonstrations Project at http://demonstrations.wolfram.com/ExploringMinimalModelsOfTheComplexityOfSecurityPrices/
- Maymin PZ (2007d) Trader dynamics in minimal models of financial complexity. Available through the Wolfram Demonstrations Project at http://demonstrations.wolfram.com/TraderDynamicsInMinimalModelsOfFinancialComplexity/
- Maymin PZ (2011a) The minimal model of financial complexity. Quant Finance 11(9):1371–1378. http://arxiv.org/pdf/0901.3812.pdf
- Maymin PZ (2011b) Markets are efficient if and only if P=NP. Algorithmic Finance 1(1):1–11Google Scholar
- Nolan JP (2005) Stable distributions: models for heavy tailed data. Birkhäuser, BostonGoogle Scholar
- Nolan JP (2009) Stable distributions: models for heavy tailed data. http://academic2.american.edu/~jpnolan/stable/chap1.pdf
- Singh SK, Maddala GS (2008) A function for size distribution of income. In: Chotikapanich D (ed) Modeling income distributions and Lorenz curves. Springer, New York, pp 24–32 (Chapter 2)Google Scholar
- Swell M (2011) Characterization of financial time series. UCL Research Note RN/11/01 UCL. http://www.cs.ucl.ac.uk/fileadmin/UCL-CS/images/Research_Student_Information/RN_11_01.pdf
- Turing AM (1936–1937) On computable numbers, with an application to the Entscheidungsprob- 1076 lem. Proc Lond Math Soc Ser 2 42:230–265. doi: 10.1112/plms/s2-42.1.2301077 Google Scholar
- Turing AM (1937) On computable numbers, with an application to the Entscheidungsproblem: 1078 a correction. Proc Lond Math Soc Ser 2 43:544–546. doi: 10.1112/plms/s2-43.6.544 Google Scholar
- Zeleny E (2005) Turing machine causal networks. Available through the Wolfram Demonstrations Project at http://demonstrations.wolfram.com/TuringMachineCausalNetworks/