IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Aggregate comparative statics

  • Acemoglu, Daron
  • Jensen, Martin Kaae

In aggregative games, each playerʼs payoff depends on her own actions and an aggregate of the actions of all the players. Many common games in industrial organization, political economy, public economics, and macroeconomics can be cast as aggregative games. This paper provides a general and tractable framework for comparative static results in aggregative games. We focus on two classes of games: (1) aggregative games with strategic substitutes and (2) nice aggregative games, where payoff functions are continuous and concave in own strategies. We provide simple sufficient conditions under which positive shocks to individual players increase their own actions and have monotone effects on the aggregate. The results are illustrated with applications to public good provision, contests, Cournot competition and technology choices in oligopoly.

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:
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

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

Volume (Year): 81 (2013)
Issue (Month): C ()
Pages: 27-49

in new window

Handle: RePEc:eee:gamebe:v:81:y:2013:i:c:p:27-49
DOI: 10.1016/j.geb.2013.03.009
Contact details of provider: Web page:

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. 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).
  2. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Richard Cornes & Roger Hartley, . "Weak Links, Good Shots And Other Public Good Games: Building On Bbv," Discussion Papers 06/09, University of Nottingham, School of Economics.
  4. Kockesen, L. & Ok, E.A. & Sethi, R., 1998. "Evolution of Interdependent Preferences in Aggregative Games," Working Papers 98-19, C.V. Starr Center for Applied Economics, New York University.
  5. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  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. Martin K. Jensen, 2006. "Aggregative Games," Discussion Papers 06-10, Department of Economics, University of Birmingham.
  8. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-80, January.
  9. Roy, Sunanda & Sabarwal, Tarun, 2012. "Characterizing stability properties in games with strategic substitutes," Games and Economic Behavior, Elsevier, vol. 75(1), pages 337-353.
  10. P. Diamond, 1980. "Aggregate Demand Management in Search Equilibrium," Working papers 268, Massachusetts Institute of Technology (MIT), Department of Economics.
  11. R Cornes & R Hartley, 2005. "The Geometry of Aggregative Games," The School of Economics Discussion Paper Series 0514, Economics, The University of Manchester.
  12. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
  13. Martin Jensen, 2010. "Aggregative games and best-reply potentials," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 45-66, April.
  14. Fraser, Clive D., 2012. "Nash equilibrium existence and uniqueness in a club model," Economics Letters, Elsevier, vol. 117(2), pages 496-499.
  15. Richard Cornes & Roger Hartley, 2009. "Fully Aggregative Games," ANU Working Papers in Economics and Econometrics 2009-505, Australian National University, College of Business and Economics, School of Economics.
  16. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  17. Daron Acemoglu, 2007. "Equilibrium Bias of Technology," Econometrica, Econometric Society, vol. 75(5), pages 1371-1409, 09.
  18. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
  19. Skaperdas, S., 1991. "Cooperation, Conflict And Power In The Absence Of Property Rights," Papers 90-91-06a, California Irvine - School of Social Sciences.
  20. Schmalensee, Richard, 1981. "Output and Welfare Implications of Monopolistic Third-Degree Price Discrimination," American Economic Review, American Economic Association, vol. 71(1), pages 242-47, March.
  21. 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).
  22. Glenn C. Loury, 1979. "Market Structure and Innovation," The Quarterly Journal of Economics, Oxford University Press, vol. 93(3), pages 395-410.
  23. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 923-946, November.
  24. Villas-Boas, J. Miguel, 1997. "Comparative Statics of Fixed Points," Journal of Economic Theory, Elsevier, vol. 73(1), pages 183-198, March.
  25. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
  26. Seade, Jesus K, 1980. "On the Effects of Entry," Econometrica, Econometric Society, vol. 48(2), pages 479-89, March.
  27. Kukushkin, Nikolai S., 1994. "A fixed-point theorem for decreasing mappings," Economics Letters, Elsevier, vol. 46(1), pages 23-26, September.
  28. Alex Possajennikov, 2003. "Evolutionary foundations of aggregate-taking behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 921-928, 06.
  29. Dixit, Avinash K, 1987. "Strategic Behavior in Contests," American Economic Review, American Economic Association, vol. 77(5), pages 891-98, December.
  30. Jack Hirshleifer, 1989. "Conflict and rent-seeking success functions: Ratio vs. difference models of relative success," Public Choice, Springer, vol. 63(2), pages 101-112, November.
  31. Kotchen, Matthew J., 2007. "Equilibrium existence and uniqueness in impure public good models," Economics Letters, Elsevier, vol. 97(2), pages 91-96, November.
  32. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
  33. 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.
  34. W. M. Gorman, 1968. "The Structure of Utility Functions," Review of Economic Studies, Oxford University Press, vol. 35(4), pages 367-390.
  35. Burkhard Schipper, 2002. "Submodularity and the Evolution of Walrasian Behavior," Bonn Econ Discussion Papers bgse4_2003, University of Bonn, Germany.
  36. Russell Cooper & Andrew John, 1988. "Coordinating Coordination Failures in Keynesian Models," The Quarterly Journal of Economics, Oxford University Press, vol. 103(3), pages 441-463.
  37. Nti, Kofi O, 1997. "Comparative Statics of Contests and Rent-Seeking Games," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 43-59, February.
  38. F. H. Hahn, 1962. "The Stability of the Cournot Oligopoly Solution," Review of Economic Studies, Oxford University Press, vol. 29(4), pages 329-331.
  39. Ausubel, Lawrence M & Deneckere, Raymond J, 1993. "A Generalized Theorem of the Maximum," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 99-107, January.
  40. Milgrom, Paul & Roberts, John, 1994. "Comparing Equilibria," American Economic Review, American Economic Association, vol. 84(3), pages 441-59, 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:eee:gamebe:v:81:y:2013:i:c:p:27-49. 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: (Shamier, Wendy)

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.