Comparative Statics with Never Increasing Correspondences
This paper studies models where the correspondences (or functions) under consideration are never increasing (or weakly decreasing) in endogenous variables, and weakly increasing in exogenous parameters. Such models include games of strategic substitutes, and include cases where additionally, some variables may be strategic complements. It is shown that the equilibrium set in such models is a non-empty, complete lattice, if, and only if, there is a unique equilibrium. For a given parameter value, a pair of distinct equilibria are never comparable. Moreover, generalizing an existing result, it is shown that when a parameter increases, no new equilibrium is smaller than any old equilibrium. (In particular, in n-player games with real-valued action spaces, symmetric equilibria increase with the parameter.) Furthermore, when functions under consideration are weakly decreasing in endogenous variables, a sufficient condition is presented that guarantees existence of increasing equilibria (symmetric or asymmetric) at a new parameter value. This condition is applied to two classes of examples.
|Date of creation:||04 May 2005|
|Date of revision:||21 Oct 2005|
|Note:||Type of Document - pdf; pages: 25|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
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.:
- 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.
- Federico Echenique, 2002.
"Comparative Statics by Adaptive Dynamics and the Correspondence Principle,"
Econometric Society, vol. 70(2), pages 833-844, March.
- Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Econometric Society World Congress 2000 Contributed Papers 1906, Econometric Society.
- Federico Echenique, 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," GE, Growth, Math methods 9912002, EconWPA.
- Federico Echenique., 2000. "Comparative Statics by Adaptive Dynamics and The Correspondence Principle," Economics Working Papers E00-273, University of California at Berkeley.
- Federico Echenique, 1999. "Comparative Statics by Adaptative Dynamics and the Correspondence Principle," Documentos de Trabajo (working papers) 2099, Department of Economics - dECON.
- Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
- 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).
- Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
- Novshek, William., 1984.
"On the Existence of Cournot Equilibrium,"
517, California Institute of Technology, Division of the Humanities and Social Sciences.
- Echenique, Federico & Sabarwal, Tarun, 2003. "Strong comparative statics of equilibria," Games and Economic Behavior, Elsevier, vol. 42(2), pages 307-314, February.
- Milgrom, P. & Shannon, C., 1991.
"Monotone Comparative Statics,"
11, Stanford - Institute for Thoretical Economics.
- Bamon, Rodrigo & Fraysse, Jean, 1985. "Existence of Cournot Equilibrium in Large Markets," Econometrica, Econometric Society, vol. 53(3), pages 587-597, May.
- Rabah Amir & Val E. Lambson, 2000.
"On the Effects of Entry in Cournot Markets,"
Review of Economic Studies,
Oxford University Press, vol. 67(2), pages 235-254.
- Rabah Amir & Val E. Lambson, 1998. "On the Effects of Entry in Cournot Markets," CIE Discussion Papers 1998-06, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
- Rabah Amir, 2000. "On the Effects of Entry in Cournot Markets," Econometric Society World Congress 2000 Contributed Papers 1475, Econometric Society.
- AMIR, Rabah & LAMBSON, Val, 1999. "On the effects of entry in Cournot markets," CORE Discussion Papers 1999059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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).
- 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.
- 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.
- Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:0505001. 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: (EconWPA)
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.