Advertisement

Annals of Operations Research

, Volume 30, Issue 1, pp 45–62 | Cite as

Adaptive approaches to stochastic programming

  • Patrick H. McAllister
Modelling Approaches

Abstract

Economists have found a need to model agents who behave in ways that are not consistent with the traditional notions of rational behavior under uncertainty but that are oriented in some looser manner toward achieving “good” outcomes. Adaptation over time in a myopic manner, rather that forward-looking optimization, has been proposed as one such model of behavior that displays bounded rationality. This paper investigates the relationship between adaptation as a model of behavior and as an algorithmic approach that has been used in computing solutions to optimization problems. It describes a specific adaptive model of behavior in discrete choice problems, one that is closely related to adaptive algorithms for optimization, and shows that this model can be fruitfully applied in studying several economic issues.

Keywords

Adaptive behavior bounded rationality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Aumann, Correlated equilibrium as an expression of Bayesian rationality, Econometrica 55 (1987) 1–18.Google Scholar
  2. [2]
    D.A. Berry and B. Fristedt,Bandit Problems: Sequential Allocation of Experiments (Chapman and Hall, London, 1985).Google Scholar
  3. [3]
    R.R. Bush and F. Mosteller,Stochastic Models for Learning (Wiley, New York, 1955).Google Scholar
  4. [4]
    G.C. Chow, Rational versus adaptive expectations in present value models, Rev. Econ. Statist. 71 (1989), 376–84.Google Scholar
  5. [5]
    G.M. Constantinides, Habit formation: A resolution of the equity premium puzzle, mimeo, University of Chicago (1988).Google Scholar
  6. [6]
    V.P. Crawford, An “evolutionary” explanation of van Huyck Battalio, and Beil's experimental results on coordination, mimeo. University of California, San Diego, Department of Economics (1989).Google Scholar
  7. [7]
    J.G. Cross,A Theory of Adaptive Economic Behavior (Cambridge University Press, New York. 1983).Google Scholar
  8. [8]
    I. Friend and M.E. Blume, The demand for risky assets, Amer. Econ. Rev. 65 (1975), 900–22.Google Scholar
  9. [9]
    D. Goldberg,Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, MA, 1989).Google Scholar
  10. [10]
    G.C. Goodwin and K.S. Sin,Adaptive Filtering, Prediction, and Control (Prentice-Hall, Englewood Cliffs, NJ, 1984).Google Scholar
  11. [11]
    J. Harsanyi and R. Selten,A General Theory of Equilibrium Selection in Games (MIT Press, Cambridge, MA, 1988).Google Scholar
  12. [12]
    D. Kahneman and A. Tversky, Judgement under uncertainty: Heuristics and biases, in:Judgement Under Uncertainty: Heuristics and Biases, eds. D. Kahneman and A. Tversky (Cambridge University Press, New York, 1982).Google Scholar
  13. [13]
    D. Kahneman and A. Tversky, Judgements of and by representativeness, in:Judgement Under Uncertainty: Heuristics and Biases, eds. D. Kahneman and A. Tversky (Cambridge University Press, New York, 1982).Google Scholar
  14. [14]
    D. Kahneman and A. Tversky (eds.),Judgement Under Uncertainty: Heuristics and Biases (Cambridge University Press, New York, 1982).Google Scholar
  15. [15]
    M. Katehakis and A.F. Veinott, Jr, The multi-armed bandit problem: Decomposition and computation. Math. Oper. Res. 12 (1987) 262–68.Google Scholar
  16. [16]
    L.R. Keller, The effects of problem representation on the sure-thing and substitution principles, Manag. Sci. 31 (1985) 738–51.Google Scholar
  17. [17]
    S. Lakshmivarahan and K.S. Narendra, Learning algorithms for two-person zero-sum stochastic games with incomplete information, Math. Oper. Res. 6 (1981) 379–86.Google Scholar
  18. [18]
    S. Lakshmivarahan and K.S. Narendra, Learning algorithms for two-person zero-sum stochastic games with incomplete information: A unified approach, SIAM J. Contr. Opt. 20 (1982) 541–52.Google Scholar
  19. [19]
    M. Machina, Choice under uncertainty: Problems solved and unsolved. J. Econ. Perspectives 1 (1987) 121–54.Google Scholar
  20. [20]
    A. Marcet and T.J. Sargent, Convergence of least squares learning mechanisms in self-referential linear stochastic models. J. Econ. Theory 48 (1989) 337–68.Google Scholar
  21. [21]
    R. Marimon, E. McGrattan, and T.J. Sargent, Money as a medium of exchange in an economy with artificially intelligent agents, mimeo, Hoover Institution, Stanford University (1989).Google Scholar
  22. [22]
    R. Mehra and E. C. Prescott, The equity premium: A puzzle, J. Monetary Econ. 15 (1985) 145–61.Google Scholar
  23. [23]
    K.S. Narendra and M.A.L. Thathachar,Learning Automata: An Introduction (Prentice-Hall, Englewood Cliffs, NJ, 1989).Google Scholar
  24. [24]
    K.S. Narendra and R.M. Wheeler, Jr, Decentralized learning in finite Markov chains, IEEE Trans. Auto. Contr. AC-31 (1986) 519–26.Google Scholar
  25. [25]
    M.F. Norman, Some convergence theorems for stochastic learning models with distance diminishing operators, J. Math. Psych. 5 (1968) 61–101.Google Scholar
  26. [26]
    L.J. Savage,The Foundations of Statistics (Wiley, New York, 1954). (Revised edition: Dover, New York, 1972).Google Scholar
  27. [27]
    S. Urjas'ev, Stochastic quasi-gradients, in:Numerical Techniques for Stochastic Optimization, Springer Series in Computational Mathematics no. 10., eds. Y. Ermoliev and R. Wets, (Springer, New York, 1988).Google Scholar
  28. [28]
    J.B. van Huyck, R. Battalio and R.O. Beil, Tacit coordination games, strategic uncertainty, and coordination failure, Amer. Econ. Rev. 80 (1990) 234–48.Google Scholar
  29. [29]
    J. von Neumann and O. Morgenstern,The Theory of Games and Economic Behavior (Princeton University Press, Princeton, NJ, 1944; 3rd, 1953).Google Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1991

Authors and Affiliations

  • Patrick H. McAllister
    • 1
  1. 1.Washington, DCUSA

Personalised recommendations