IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Characterizing Stability Properties in Games with Strategic Substitutes

  • Sunanda Roy

    (Department of Economics, Iowa State University)

  • Tarun Sabarwal

    (Department of Economics, University of Kansas)

In games with strategic substitutes (GSS), convergence of the best response dynamic starting from the inf (or sup) of the strategy space is equivalent to global stability (convergence of every adaptive dynamic to the same pure strategy Nash equilibrium). Consequently, in GSS, global stability can be analyzed using a single best response dynamic. Moreover, in GSS, global stability is equivalent to dominance solvability, showing that in this class of games, two different foundations for robustness of predicted outcomes are equivalent, and both can be checked using a single best response dynamic. These equivalences are useful to study stability of equilibria in a variety of applications. Furthermore, in parameterized GSS, under natural conditions, dynamically stable equilibrium selections can be viewed in terms of monotone selections of equilibria. Several examples are provided.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201003.pdf
Download Restriction: no

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201003.

as
in new window

Length: 29 pages
Date of creation: Jul 2010
Date of revision: Oct 2011
Handle: RePEc:kan:wpaper:201003
Contact details of provider: Postal: 415 Snow Hall, Lawrence, KS 66045
Phone: (785) 864-3501
Fax: (785) 864-5270
Web page: http://www2.ku.edu/~kuwpaper/
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 514, David K. Levine.
  2. Okuguchi, Koji & Yamazaki, Takeshi, 2008. "Global stability of unique Nash equilibrium in Cournot oligopoly and rent-seeking game," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1204-1211, April.
  3. AMIR, Rabah & WOODERS, John, 1997. "One-way spillovers, endogenous innovator/imitator roles and research joint ventures," CORE Discussion Papers 1997027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Karp, Larry & Lee, In Ho & Mason, Robin, 2003. "A global game with strategic substitutes and complements," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt09h2490x, Department of Agricultural & Resource Economics, UC Berkeley.
  5. Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley.
  6. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, 03.
  7. AMIR, Rabah, 1994. "Cournot Oligopoly and the Theory of Supermodular Games," CORE Discussion Papers 1994013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Roy, Sunanda & Sabarwal, Tarun, 2006. "On the (non-)lattice structure of the equilibrium set in games with strategic substitutes," MPRA Paper 4120, University Library of Munich, Germany, revised 23 May 2007.
  9. al-Nowaihi, A. & Levine, P. L., 1985. "The stability of the cournot oligopoly model: A reassessment," Journal of Economic Theory, Elsevier, vol. 35(2), pages 307-321, August.
  10. Echenique, Federico, 2001. "A Characterization of Strategic Complementarities," Department of Economics, Working Paper Series qt5w13s4z2, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  11. Edlin, Aaron S. & Shannon, Chris, 1998. "Strict Monotonicity in Comparative Statics," Journal of Economic Theory, Elsevier, vol. 81(1), pages 201-219, July.
  12. Amir, Rabah & Lambson, Val E, 2000. "On the Effects of Entry in Cournot Markets," Review of Economic Studies, Wiley Blackwell, vol. 67(2), pages 235-54, April.
  13. Acemoglu, Daron & Jensen, Martin Kaae, 2009. "Aggregate Comparative Statics," CEPR Discussion Papers 7254, C.E.P.R. Discussion Papers.
  14. John Quah & Bruno Strulovici, 2007. "Comparative Statics, Informativeness, and the Interval Dominance Order," Economics Series Working Papers 2007-WO4, University of Oxford, Department of Economics.
  15. Zimper, Alexander, 2006. "Uniqueness conditions for strongly point-rationalizable solutions to games with metrizable strategy sets," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 729-751, September.
  16. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  17. Sergiu Hart & Andreu Mas-Colell, 1997. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Game Theory and Information 9703006, EconWPA, revised 24 Mar 1997.
  18. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer, vol. 43(1), pages 45-66, April.
  19. Roy, Sunanda & Sabarwal, Tarun, 2009. "Monotone Comparative Statics for Games With Strategic Substitutes," Staff General Research Papers 31558, Iowa State University, Department of Economics.
  20. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  21. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  22. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
  23. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
  24. Roy, Sunanda & Sabarwal, T, 2008. "On the (Non)-Lattice Structure of Equilibrium Sets in Games with Strategic Substitutes," Staff General Research Papers 13103, Iowa State University, Department of Economics.
  25. Amir, Rabah & Garcia, Filomena & Knauff, Malgorzata, 2010. "Symmetry-breaking in two-player games via strategic substitutes and diagonal nonconcavity: A synthesis," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1968-1986, September.
  26. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
  27. Milgrom, P. & Shannon, C., 1991. "Monotone Comparative Statics," Papers 11, Stanford - Institute for Thoretical Economics.
  28. Alexander Zimper, 2005. "A fixed point characterization of the dominancesolvability of lattice games with strategic substitutes," Working Papers 32, Economic Research Southern Africa.
  29. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181, March.
  30. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
  31. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  32. Lippman, Steven A. & Mamer, John W. & McCardle, Kevin F., 1987. "Comparative statics in non-cooperative games via transfinitely iterated play," Journal of Economic Theory, Elsevier, vol. 41(2), pages 288-303, April.
  33. Zhou Lin, 1994. "The Set of Nash Equilibria of a Supermodular Game Is a Complete Lattice," Games and Economic Behavior, Elsevier, vol. 7(2), pages 295-300, September.
  34. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:kan:wpaper:201003. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Jianbo Zhang)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.