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Mathematics and Financial Economics

, Volume 5, Issue 3, pp 161–184 | Cite as

Evolutionary finance and dynamic games

  • Rabah Amir
  • Igor V. EvstigneevEmail author
  • Thorsten Hens
  • Le Xu
Article

Abstract

The paper examines a game-theoretic evolutionary model of an asset market with endogenous equilibrium asset prices. Assets pay dividends that are partially consumed and partially reinvested. The investors use general, adaptive strategies (portfolio rules), distributing their wealth between assets, depending on the exogenous states of the world and the observed history of the game. The main objective of the work is to identify strategies, allowing an investor to “survive”, i.e. to possess a positive, bounded away from zero, share of market wealth over the whole infinite time horizon. This work brings together recent studies on evolutionary finance with the classical topic of non-cooperative market games.

Keywords

Evolutionary finance Dynamic games Stochastic games Survival strategies 

JEL Classification

C73 D52 G11 

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References

  1. 1.
    Algoet P.H., Cover T.M.: Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. Ann. Probab. 16, 876–898 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Amir R., Sahi S., Shubik M., Yao S.: A strategic market game with complete markets. J. Econ. Theory 51, 126–143 (1990)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Amir, R., Evstigneev, I.V., Hens, T., Schenk-Hoppé, K.R.: Market selection and survival of investment strategies. J. Math. Econ. 41, 105–122 (2005) (special issue on Evolutionary Finance)Google Scholar
  4. 4.
    Amir, R., Evstigneev, I.V., Schenk-Hoppé, K.R.: Asset market games of survival: a synthesis of evolutionary and dynamic games. Swiss Finance Institute research paper no. 08-31 (2010)Google Scholar
  5. 5.
    Arkin V.I., Evstigneev I.V.: Stochastic Models of Control and Economic Dynamics. Academic Press, London (1987)Google Scholar
  6. 6.
    Arthur W.B., Holland J.H., LeBaron B., Palmer R.G., Taylor P.: Asset pricing under endogenous expectations in an artificial stock market. In: Arthur, W.B., Durlauf, S., Lane, D. (eds.) The Economy as an Evolving Complex System, vol. II, pp. 15–44. Addison Wesley, Reading (1997)Google Scholar
  7. 7.
    Blume L., Easley D.: Evolution and market behavior. J. Econ. Theory 58, 9–40 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Breiman, L.: Optimal gambling systems for favorable games. In: Fourth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 65–78. University of California Press, Berkeley (1961)Google Scholar
  9. 9.
    Brock, A.W., Hommes, C.H., Wagener, F.O.O.: Evolutionary dynamics in markets with many trader types. J. Math. Econ. 41, 7–42 (2005) (special issue on Evolutionary Finance)Google Scholar
  10. 10.
    Dempster M.A.H., Evstigneev I.V., Schenk-Hoppé K.R.: Volatility-induced financial growth. Quant. Finance 7, 151–160 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Dempster M.A.H., Evstigneev I.V., Schenk-Hoppé K.R.: Financial markets. The joy of volatility. Quant. Finance 8, 1–3 (2008)zbMATHCrossRefGoogle Scholar
  12. 12.
    Dempster M.A.H., Mitra G., Pflug G.: Quantitative Fund Management. Chapman and Hall/CRC Financial Mathematics Series. Taylor and Francis Group, Boca Raton (2009)Google Scholar
  13. 13.
    Dempster, M.A.H., Evstigneev, I.V., Schenk-Hoppé, K.R.: Growing wealth with fixed-mix strategies. In: MacLean, L.C., Thorp, E.O., Ziemba, W.T. (eds.) The Kelly Capital Growth Investment Criterion: Theory and Practice, pp. 427–455. World Scientific, Singapore (2011)Google Scholar
  14. 14.
    Dubey P., Geanakoplos J., Shubik M.: The revelation of information in strategic market games. A critique of rational expectations equilibrium. J. Math. Econ. 16, 105–137 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Evstigneev I.V., Hens T., Schenk-Hoppé K.R.: Evolutionary stable stock markets. Econ. Theory 27, 449–468 (2006)zbMATHCrossRefGoogle Scholar
  16. 16.
    Evstigneev I.V., Hens T., Schenk-Hoppé K.R.: Globally evolutionarily stable portfolio rules. J. Econ. Theory 140, 197–228 (2008)zbMATHCrossRefGoogle Scholar
  17. 17.
    Evstigneev I.V., Hens T., Schenk-Hoppé K.R.: Evolutionary finance. In: Hens, T., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution, Chapter 9, pp. 507–566. Elsevier, Amsterdam (2009)CrossRefGoogle Scholar
  18. 18.
    Evstigneev, I.V., Hens, T., Schenk-Hoppé, K.R.: Local stability analysis of a stochastic evolutionary financial market model with a risk-free asset. Swiss Finance Institute research paper no. 10–36 (2011)Google Scholar
  19. 19.
    Farmer J.D., Lo A.W.: Frontiers of finance: evolution and efficient markets. Proc. Natl. Acad. Sci. USA 96, 9991–9992 (1999)CrossRefGoogle Scholar
  20. 20.
    Gale D.: On optimal development in a multi-sector economy. Rev. Econ. Stud. 34, 1–18 (1967)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Grandmont, J.-M. (ed.): Temporary Equilibrium. Academic Press, San Diego (1988)zbMATHGoogle Scholar
  22. 22.
    Hakansson N.H., Ziemba W.T.: Capital growth theory. In: Jarrow, R.A., Maksimovic, V., Ziemba, W.T. (eds.) Handbooks in Operations Research and Management Science, vol. 9: Finance, pp. 65–86. Elsevier, Amsterdam (1995)Google Scholar
  23. 23.
    Kelly J.L.: A new interpretation of information rate. Bell Syst. Techn. J. 35, 917–926 (1956)Google Scholar
  24. 24.
    Kuhn D., Luenberger D.G.: Analysis of the rebalancing frequency in log-optimal portfolio selection. Quant. Finance 10, 221–234 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    LeBaron B., Arthur W.B., Palmer R.: Time series properties of an artificial stock market. J. Econ. Dyn. Control 23, 1487–1516 (1999)zbMATHCrossRefGoogle Scholar
  26. 26.
    Luce R., Raiffa H.: Games and Decisions, 2nd edn. Dover, New York (1989)Google Scholar
  27. 27.
    Lux T.: Stochastic behavioral asset pricing models and the stylized facts. In: Hens, T., Schenk-Hoppé, K.R. (eds.) Handbook of Financial Markets: Dynamics and Evolution, Chapter 3, pp. 161–211. Elsevier, Amsterdam (2009)CrossRefGoogle Scholar
  28. 28.
    Magill M., Quinzii M.: Theory of Incomplete Markets. MIT Press, Cambridge (1996)Google Scholar
  29. 29.
    Maitra A., Sudderth W.D.: Discrete Gambling and Stochastic Games. Springer, New York (1996)zbMATHGoogle Scholar
  30. 30.
    Marshall A.: Principles of Economics, 8th edn. Macmillan, London (1949)Google Scholar
  31. 31.
    Maynard Smith J.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)zbMATHGoogle Scholar
  32. 32.
    McKenzie, L.W.: Optimal economic growth, turnpike theorems and comparative dynamics. In: Arrow, K.J., Intrilligator, M.D. (eds.) Handbook of Mathematical Economics, vol. III, pp. 1281–1355. Amsterdam, North Holland (1986)Google Scholar
  33. 33.
    Nikaido H.: Convex Structures and Economic Theory. Academic Press, New York (1968)zbMATHGoogle Scholar
  34. 34.
    Radner R.: Existence of equilibrium of plans, prices, and price expectations in a sequence of markets. Econometrica 40, 289–303 (1972)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Sahi S., Yao S.: The noncooperative equilibria of a trading economy with complete markets and consistent prices. J. Math. Econ. 18, 325–346 (1989)MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Samuelson L.: Evolutionary Games and Equilibrium Selection. MIT Press, Cambridge (1997)zbMATHGoogle Scholar
  37. 37.
    Samuelson P.A.: Foundations of Economic Analysis. Harvard University Press, Cambridge (1947)zbMATHGoogle Scholar
  38. 38.
    Schlicht E.: Isolation and Aggregation in Economics. Springer, Berlin (1985)zbMATHCrossRefGoogle Scholar
  39. 39.
    Secchi P., Sudderth W.D.: Stay-in-a-set games. Int. J. Game Theory 30, 479–490 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Shapley L.S.: Stochastic games. Proc. Natl. Acad. Sci. USA 39, 1095–1100 (1953)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Shapley, L.S.: Noncooperative general exchange. In: Lin, S.A.Y. (ed.) Theory and Measurement of Economic Externalities, pp. 155–175. Academic Press, New York (1976)Google Scholar
  42. 42.
    Shapley L.S., Shubik M.: Trade using one commodity as a means of payment. J. Political Econ. 85, 937–968 (1977)CrossRefGoogle Scholar
  43. 43.
    Shubik M.: A theory of money and financial institutions. Fiat money and noncooperative equilibrium in a closed economy. Int. J. Game Theory 1, 243–268 (1972)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Rabah Amir
    • 1
  • Igor V. Evstigneev
    • 2
    Email author
  • Thorsten Hens
    • 3
    • 4
  • Le Xu
    • 5
  1. 1.Department of EconomicsUniversity of ArizonaTucsonUSA
  2. 2.Department of Economics, School of Social SciencesUniversity of ManchesterManchesterUK
  3. 3.Department of Banking and FinanceUniversity of ZurichZurichSwitzerland
  4. 4.Department of Finance and ManagementNorwegian School of Economics and Business AdministrationBergenNorway
  5. 5.Department of Strategy and Policy, Business SchoolNational University of SingaporeSingaporeSingapore

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