Skip to main content

Equilibrium Selection via Adaptation: Using Genetic Programming to Model Learning in a Coordination Game

  • Chapter
Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 7))

Abstract

This paper models adaptive learning behavior in a simple coordination game that Van Huyck, Cook and Battalio (1994) have investigated in a controlled laboratory setting with human subjects. We consider how populations of arti- ficially intelligent players behave when playing the same game. We use the genetic programming paradigm, as developed by Koza (1992, 1994), to model how a population of players might learn over time. In genetic programming one seeks to breed and evolve highly fit computer programs that are capable of solving a given problem. In our application, each computer program in the population can be viewed as an individual agent’s forecast rule. The various forecast rules (programs) then repeatedly take part in the coordination game evolving and adapting over time according to principles of natural selection and population genetics.We argue that the genetic programming paradigm that we use has certain advantages over other models of adaptive learning behavior in the context of the coordination game that we consider. We find that the pattern of behavior generated by our population of artificially intelligent players is remarkably similar to that followed by the human subjects who played the same game. In particular, we find that a steady state that is theoretically unstable under a myopic, best-response learning dynamic turns out to be stable under our genetic-programming-based learning system, in accordance with Van Huyck et al.’s (1994) finding using human subjects. We conclude that genetic programming techniques may serve as a plausible mechanism for modeling human behavior, and may also serve as a useful selection criterion in environments with multiple equilibria.

This project was initiated while Duffy was visiting National Chengchi University. A preliminary version of this paper, Chen, Duffy and Yeh (1996), was presented at the {cn1996 Evolutionary Programming Conference}.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allen F. and Karjalainen R., 1999. Using Genetic Algorithms to Find Technical Trading Rules. Journal of Financial Economics, 51(2), 245–71.

    Article  Google Scholar 

  2. Angeline P., (1994). Genetic Programming and Emergent Intelligence. Chapter 4 of Kinnear (1994).

    Google Scholar 

  3. Arifovic J., (1994). Genetic Algorithm Learning and the Cobweb Model. Journal of Economic Dynamics and Control, 18, 3–28.

    Article  MATH  Google Scholar 

  4. Arifovic J., (1995). Genetic Algorithms and Inflationary Economies. Journal of Monetary Economics, 36, 219–243.

    Article  Google Scholar 

  5. Arifovic J., (1996). The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economies. Journal of Political Economy, 104, 510–541.

    Article  Google Scholar 

  6. Arifovic J., (1997). Strategic Uncertainty and the Genetic Algorithm Adaptation. In H. Amman et al. (eds.), Computational Approaches to Economic Problems. Boston: Kluwer Academic Press, 225–36.

    Google Scholar 

  7. Arthur W. B., Holland J. H., LeBaron B., Palmer R. and Tayler P., (1997). Asset Pricing Under Endogenous Expectations in an Artificial Stock Market. In W.B. Arthur et al. (eds.), The Economy as a Evolving Complex System II. Reading, MA: Addison-Wesley, 15–44.

    Google Scholar 

  8. Birchenhall C. R., (1995). Genetic Algorithms, Classifier Systems and Genetic Programming and Their Use in Models of Adaptive Behavior and Learning. Economic Journal, 105, 788–795.

    Article  Google Scholar 

  9. Bray M., (1982). Learning, Estimation, and the Stability of Rational Expectations. Journal of Economic Theory, 26, 318–339.

    Article  MATH  MathSciNet  Google Scholar 

  10. Bullard J. and Duffy J., (1998a). A Model of Learning and Emulation with Artificial Adaptive Agents. Journal of Economic Dynamics and Control, 22, 179–207.

    Article  MathSciNet  Google Scholar 

  11. Bullard J. and Duffy J., (1998). On Learning and the Stability of Cycles. Macroeconomic Dynamics, 2, 22–48.

    MATH  Google Scholar 

  12. Chen S. and Yeh C., (1997a). Toward a Computable Approach to the Efficient Market Hypothesis: An Application of Genetic Programming. Journal of Economic Dynamics and Control, 21, 1043–1063.

    Article  MATH  MathSciNet  Google Scholar 

  13. Chen S. and Yeh C., (1997b). On the Coordination and Adaptability of the Large Economy: An Application of Genetic Programming to the Cobweb Model. In P. Angeline and K.E. Kinnear, Jr., (eds.), Advances in Genetic Programming II, Chapter 22. Cambridge, MA: MIT Press.

    Google Scholar 

  14. Chen S., Duffy J. and Yeh C., (1996). Genetic Programming in the Coordination Game with a Chaotic Best-Response Function. In: Proceedings of the 1996 Evolutionary Programming Conference, San Diego, CA.

    Google Scholar 

  15. Cooper R., DeJong D., Forsythe R. and Ross T., (1990). Selection Criterion in Coordination Games: Some Experimental Results. American Economic Review, 80, 218–233.

    Google Scholar 

  16. Crawford V. P., (1991). An Evolutionary Interpretation of Van Huyck, Battalio and Beil’s Experimental Results on Coordination. Games and Economic Behavior, 3, 25–59.

    Article  MATH  Google Scholar 

  17. Crawford V. P., (1995). Adaptive Dynamics in Coordination Games. Econometrica, 63, 103–143.

    Article  MATH  MathSciNet  Google Scholar 

  18. Dawid H., (1996), Adaptive Learning by Genetic Algorithms, Lecture Notes in Economics and Mathematical Systems No. 441. New York: Springer.

    MATH  Google Scholar 

  19. Devaney R. L., (1989). An Introduction to Chaotic Dynamical Systems, 2nd Ed.. Reading, MA: Addison-Wesley.

    MATH  Google Scholar 

  20. Dworman G., Kimbrough S. O. and Laing J. D., (1996). On Automated Discovery of Models Using Genetic Programming: Bargaining in a Three-Agent Coalitions Game. Journal of Management Information Systems, 12, 97–125.

    Google Scholar 

  21. Goldberg D. E., (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Reading, MA: Addison-Wesley.

    MATH  Google Scholar 

  22. Holland J. H., (1975). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. Ann Arbor: University of Michigan Press.

    Google Scholar 

  23. Kagel J. H. and Roth A. E., (1995), eds., Handbook of Experimental Economics. Princeton, NJ: Princeton University Press.

    Google Scholar 

  24. Kinnear K. E., Jr., (1994), (ed.) Advances in Genetic Programming. Cambridge, MA: MIT Press.

    Google Scholar 

  25. Koza J. R., (1992). Genetic Programming. Cambridge, MA: MIT Press.

    MATH  Google Scholar 

  26. Koza J. R., (1994). Genetic Programming II. Cambridge, MA: MIT Press.

    MATH  Google Scholar 

  27. Kreps D. M., (1990). Game Theory and Economic Modelling. New York: Oxford University Press.

    Google Scholar 

  28. Lucas R. E., Jr., (1986). Adaptive Behavior and Economic Theory. Journal of Business, 59, S401–S426.

    Article  Google Scholar 

  29. Marcet A. and Sargent T. J., (1989). Convergence of Least Squares Learning Mechanisms in Self Referential Linear Stochastic Models. Journal of Economic Theory, 48, 337–368.

    Article  MATH  MathSciNet  Google Scholar 

  30. Marimon R., (1997). Learning From Learning in Economics. In D.M. Kreps and K.F. Wallis, eds., Advances in Economics and Econometrics: Theory and Applications, Vol. 1, Seventh World Congress, Econometric Society Monographs, No. 26, Cambridge: Cambridge University Press.

    Google Scholar 

  31. Marimon R., Spear S. E. and Sunder S., (1993). Expectationally Driven Market Volatility: An Experimental Study. Journal of Economic Theory, 61, 74–103.

    Article  MATH  Google Scholar 

  32. Miller J. H., (1996). The Coevolution of Automata in the Repeated Prisoner’s Dilemma. Journal of Economic Behavior and Organization, 29, 87–112.

    Article  Google Scholar 

  33. Mitchell M., (1996). An Introduction to Genetic Algorithms. Cambridge, MA: MIT Press.

    Google Scholar 

  34. Neely C. J., Weller P. and Dittmar. R., (1997) Is Technical Analysis in the Foreign Exchange Market Profitable?: A Genetic Programming Approach. Journal of Financial and Quantitative Analysis, 32, 405–26.

    Article  Google Scholar 

  35. Sargent T. J., (1993), Bounded Rationality in Macroeconomics. New York: Oxford University Press.

    Google Scholar 

  36. Siegel S. and Castellan N. J., Jr., (1988). Nonparametric Statistics for the Behavioral Sciences, 2nd Ed. New York: McGraw Hill.

    Google Scholar 

  37. Tesfatsion L., (1997). A Trade Network Game with Endogenous Partner Selection. In H. Amman et al. (eds.), Computational Approaches to Economic Problems. Boston: Kluwer, 249–269.

    Google Scholar 

  38. Van Huyck J. B., Battalio R. C. and Beil R., (1990). Tacit Coordination Games, Strategic Uncertainty and Coordination Failure. American Economic Review, 80, 234–248.

    Google Scholar 

  39. Van Huyck J. B., Battalio R. C. and Beil R., (1991). Strategic Uncertainty, Equilibrium Selection Principles and Coordination Failure in Average Opinion Games. Quarterly Journal of Economics, 106, 885–910.

    Article  MATH  Google Scholar 

  40. Van Huyck J. B., Cook., J. P. and Battalio R.C., (1994). Selection Dynamics, Asymptotic Stability, and Adaptive Behavior. Journal of Political Economy, 102, 975–1005.

    Article  Google Scholar 

  41. Van Huyck J. B., Battalio., R. C. and Rankin F.W., (1996). Selection Dynamics and Adaptive Behavior Without Much Information. Working paper, Texas A&M University.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Birkhäuser Boston

About this chapter

Cite this chapter

Chen, SH., Duffy, J., Yeh, CH. (2005). Equilibrium Selection via Adaptation: Using Genetic Programming to Model Learning in a Coordination Game. In: Nowak, A.S., Szajowski, K. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 7. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4429-6_30

Download citation

Publish with us

Policies and ethics