Skip to main content

Heterogeneous Interacting Economic Agents and Stochastic Games

  • Conference paper
Heterogenous Agents, Interactions and Economic Performance

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 521))

  • 169 Accesses

Abstract

Stochastic games offer a rich mathematical structure that makes it possible to analyze situations with heterogeneous and interacting economic agents. Depending on the actions of the economic agents, the economic environment changes from one period to another. We focus on stationary equilibrium, the simplest form of behavior that is consistent with rationality. Since the number of stationary equilibria abound, we present the stochastic tracing procedure, a method to select equilibria. Since stationary equilibria are difficult to characterize analytically, we also present a numerical algorithm by which they can be computed. The algorithm is constructed in such a way that the equilibrium selected by the stochastic tracing procedure is computed. We illustrate the usefulness of this approach by showing how it leads to new insights in the theory of dynamic oligopoly.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Allgower EL and K Georg (1990) Numerical Continuation Methods: An Introduction. Springer-Verlag, Berlin

    Book  Google Scholar 

  2. Allgower EL and K Georg (1993) Continuation and Path Following. Acta Numerica, 1–64

    Google Scholar 

  3. Allgower EL and K Georg (1997) Numerical Path Following. Handbook of Numerical Analysis, 5:3–208

    Article  Google Scholar 

  4. Breton M (1991) Algorithms for Stochastic Games. In Stochastic Games and Related Topics, TES Raghavan, TS Ferguson, T Parthasarathy, and OJ Vrieze (eds.), Series C: Game Theory, Mathematical Programming and Operations Research, 45–57

    Google Scholar 

  5. Breton M, JA Filar, A Haurie, and TA Schultz (1986) On the computation of Equilibria in Discounted Games. In Dynamic Games and Applications in Economics, T Basar (ed.), Lecture Notes on Economics and Mathematical Systems 205, Springer-Verlag, Berlin

    Google Scholar 

  6. Damme E van (1999) Game Theory: The Next Stage. In Economics Beyond the Millenium, AP Kirman and LA Gérard-Varet (eds.), Oxford University Press, 184–214

    Google Scholar 

  7. Filar JA, TA Schultz, F Thuijsman, and OJ Vrieze (1991) Nonlinear Programming and Stationary Equilibria in Stochastic Games. Mathematical Programming, 50: 227–237

    Article  Google Scholar 

  8. Filar JA and OJ Vrieze (1997) Competitive Markov Decision Processes. Springer-Verlag, New York

    Google Scholar 

  9. Fink AM (1964) Equilibrium in a Stochastic n-Person Game. Journal of Science of Hiroshima University Series A-I, 28:89–93

    Google Scholar 

  10. Garcia CB and WI Zangwill (1981) Pathways to Solutions, Fixed Points, and Equilibria. Prentice Hall, Englewood Cliffs

    Google Scholar 

  11. Haller H and R Lagunoff (2000) Genericity and Markovian Behavior in Stochastic Games. Econometrica, 68:1231–1248

    Article  Google Scholar 

  12. Harsanyi JC and R Selten (1988) A General Theory of Equilibrium Selection in Games. MIT Press, Cambridge, Massachusetts

    Google Scholar 

  13. Herings PJJ and RJAP Peeters (2000) Stationary Equilibria in Stochastic Games: Structure, Selection, and Computation. METEOR Research Memorandum 00/031, Universiteit Maastricht, Maastricht

    Google Scholar 

  14. Herings PJJ and RJAP Peeters (2001) Equilibrium Selection in Stochastic Games. METEOR Research Memorandum 01/019, Universiteit Maastricht, Maastricht

    Google Scholar 

  15. Herings PJJ, RJAP Peeters, and MP Schinkel (2001) Intertemporal Market Division: A Case of Alternating Monopoly. METEOR Research Memorandum 01/021, Universiteit Maastricht, Maastricht

    Google Scholar 

  16. Judd KL (1997) Computational Economics and Economic Theory: Substitutes or Complements? Journal of Economic Dynamics and Control, 21:907–942

    Article  Google Scholar 

  17. Judd KL (1998) Numerical Methods in Economics. MIT Press, Cambridge MA

    Google Scholar 

  18. Lemke CE and JT Howson Jr. (1964) Equilibrium Points of Bimatrix Games. SIAM Journal on Applied Mathematics, 12:413–423

    Article  Google Scholar 

  19. Maskin E and J Tirole (2001) Markov Perfect Equilibrium, I: Observable Actions. Journal of Economic Theory, 100:191–219

    Article  Google Scholar 

  20. McLennan A (1999) The Expected Number of Nash Equilibria of a Normal Form Game, mimeo

    Google Scholar 

  21. Neyman A and S Sorin (2001) Stochastic Games. Proceedings of the 1999 NATO Summer Institute on Stochastic Games held at Stony Brook, forthcoming

    Google Scholar 

  22. Parthasarathy T and TES Raghavan (1981) An Orderfield Property for Stochastic Games when One Player Controls Transition Probabilities. Journal of Optimization Theory and Applications, 33:375–392

    Article  Google Scholar 

  23. Schultz TA (1986) Mathematical Programming and Stochastic Games. Ph.D. Thesis, The John Hopkins University, Baltimore, Maryland

    Google Scholar 

  24. Shapley LS (1953) Stochastic Games. Proceedings of the National Academy of Sciences, 39:1095–1100

    Article  Google Scholar 

  25. Sobel MJ (1971) Non-cooperative Stochastic Games. The Annals of Mathematical Statistics, 42:1930–1935

    Article  Google Scholar 

  26. Takahashi M (1964) Equilibrium Points of Stochastic, Noncooperative n-Person Games. Journal of Science of Hiroshima University Series A-I, 28:95–99

    Google Scholar 

  27. Watson LT, SC Billups, and AP Morgan (1987) HOMPACK: A Suite for Codes of Globally Convergent Homotopy Algorithms. ACM Transactions on Mathematical Software, 13:281–310

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Herings, P.JJ., Peeters, R.J.A.P. (2003). Heterogeneous Interacting Economic Agents and Stochastic Games. In: Cowan, R., Jonard, N. (eds) Heterogenous Agents, Interactions and Economic Performance. Lecture Notes in Economics and Mathematical Systems, vol 521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55651-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-55651-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44057-4

  • Online ISBN: 978-3-642-55651-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics