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Characterizing stability properties in games with strategic substitutes

  • Roy, Sunanda
  • Sabarwal, Tarun

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.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 75 (2012)
Issue (Month): 1 ()
Pages: 337-353

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Handle: RePEc:eee:gamebe:v:75:y:2012:i:1:p:337-353
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  1. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  2. Federico Echenique, 2001. "A characterization of strategic complementarities," Documentos de Trabajo (working papers) 0501, Department of Economics - dECON.
  3. 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).
  4. Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Econometric Society World Congress 2000 Contributed Papers 1906, Econometric Society.
  5. 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.
  6. Roy, Sunanda & Sabarwal, Tarun, 2010. "Monotone comparative statics for games with strategic substitutes," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 793-806, September.
  7. Rabah Amir & John Wooders, 1998. "One-Way Spillovers, Endogenous Innovator/Imitator Roles and Research Jointventures," CIE Discussion Papers 1998-10, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
  8. Aaron S. Edlin and Chris Shannon., 1995. "Strict Monotonicity in Comparative Statics," Economics Working Papers 95-238, University of California at Berkeley.
  9. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  10. D. B. Bernheim, 2010. "Rationalizable Strategic Behavior," Levine's Working Paper Archive 661465000000000381, David K. Levine.
  11. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
  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. 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.
  14. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
  15. Sergiu Hart & Andreu Mas-Colell, 1996. "A simple adaptive procedure leading to correlated equilibrium," Economics Working Papers 200, Department of Economics and Business, Universitat Pompeu Fabra, revised Dec 1996.
  16. 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.
  17. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer, vol. 43(1), pages 45-66, April.
  18. 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.
  19. John K.-H. Quah & Bruno Strulovici, 2007. "Comparative Statics, Informativeness, and the Interval Dominance Order," Economics Papers 2007-W04, Economics Group, Nuffield College, University of Oxford.
  20. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  21. 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.
  22. Karp, Larry & Lee, In Ho & Mason, Robin, 2003. "A global game with strategic substitutes and complements," CUDARE Working Paper Series 940, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  23. 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.
  24. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, 03.
  25. Shannon, Chris, 1995. "Weak and Strong Monotone Comparative Statics," Economic Theory, Springer, vol. 5(2), pages 209-27, March.
  26. Young, H. Peyton, 2004. "Strategic Learning and its Limits," OUP Catalogue, Oxford University Press, number 9780199269181.
  27. Alexander Zimper, 2007. "A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes," International Journal of Game Theory, Springer, vol. 36(1), pages 107-117, September.
  28. 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.
  29. 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.
  30. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  31. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, June.
  32. 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.
  33. 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.
  34. 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.
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