IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

A Cognitive Hierarchy Model of Games

Listed author(s):
  • Colin F. Camerer
  • Teck-Hua Ho
  • Juin-Kuan Chong

Players in a game are "in equilibrium" if they are rational, and accurately predict other players' strategies. In many experiments, however, players are not in equilibrium. An alternative is "cognitive hierarchy" (CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k - 1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games.

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://hdl.handle.net/10.1162/0033553041502225
Download Restriction: Access to full text is restricted to subscribers.

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 Oxford University Press in its journal The Quarterly Journal of Economics.

Volume (Year): 119 (2004)
Issue (Month): 3 ()
Pages: 861-898

as
in new window

Handle: RePEc:oup:qjecon:v:119:y:2004:i:3:p:861-898.
Contact details of provider:

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. Colin Camerer & Teck-Hua Ho & Juin Kuan Chong, 2003. "A cognitive hierarchy theory of one-shot games: Some preliminary results," Levine's Bibliography 506439000000000495, UCLA Department of Economics.
  2. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
  3. Rosenthal, Robert W, 1989. "A Bounded-Rationality Approach to the Study of Noncooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 273-291.
  4. Devetag, Giovanna & Warglien, Massimo, 2003. "Games and phone numbers: Do short-term memory bounds affect strategic behavior?," Journal of Economic Psychology, Elsevier, vol. 24(2), pages 189-202, April.
  5. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521570176, October.
  6. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
  7. Antoni Bosch-Domènech & José G. Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, Two, (Three), Infinity, ...: Newspaper and Lab Beauty-Contest Experiments," American Economic Review, American Economic Association, vol. 92(5), pages 1687-1701, December.
  8. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
  9. Vincent P. Crawford, 2003. "Lying for Strategic Advantage: Rational and Boundedly Rational Misrepresentation of Intentions," American Economic Review, American Economic Association, vol. 93(1), pages 133-149, March.
  10. Banks Jeffrey & Camerer Colin & Porter David, 1994. "An Experimental Analysis of Nash Refinements in Signaling Games," Games and Economic Behavior, Elsevier, vol. 6(1), pages 1-31, January.
  11. Teck-Hua Ho & Keith Weigelt, 1996. "Task Complexity, Equilibrium Selection, and Learning: An Experimental Study," Management Science, INFORMS, vol. 42(5), pages 659-679, May.
  12. Cooper, David J. & Van Huyck, John B., 2003. "Evidence on the equivalence of the strategic and extensive form representation of games," Journal of Economic Theory, Elsevier, vol. 110(2), pages 290-308, June.
  13. Weizsacker, Georg, 2003. "Ignoring the rationality of others: evidence from experimental normal-form games," Games and Economic Behavior, Elsevier, vol. 44(1), pages 145-171, July.
  14. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
  15. Mookherjee, Dilip & Sopher, Barry, 1997. "Learning and Decision Costs in Experimental Constant Sum Games," Games and Economic Behavior, Elsevier, vol. 19(1), pages 97-132, April.
  16. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  17. Brit Grosskopf & Rosemarie Nagel, 2007. "Rational reasoning or adaptive behavior? Evidence from two-person beauty contest games," Economics Working Papers 1068, Department of Economics and Business, Universitat Pompeu Fabra.
  18. Tang, Fang-Fang, 2001. "Anticipatory learning in two-person games: some experimental results," Journal of Economic Behavior & Organization, Elsevier, vol. 44(2), pages 221-232, February.
  19. David I. Laibson & Xavier Gabaix, 2000. "A Boundedly Rational Decision Algorithm," American Economic Review, American Economic Association, vol. 90(2), pages 433-438, May.
  20. Milgrom, Paul & Stokey, Nancy, 1982. "Information, trade and common knowledge," Journal of Economic Theory, Elsevier, vol. 26(1), pages 17-27, February.
  21. Daniel Kahneman, 2003. "Maps of Bounded Rationality: Psychology for Behavioral Economics," American Economic Review, American Economic Association, vol. 93(5), pages 1449-1475, December.
  22. Gabaix, Xavier & Laibson, David Isaac & Moloche, Guillermo & Stephen, Weinberg, 2003. "The allocation of attention: theory and evidence," MPRA Paper 47339, University Library of Munich, Germany.
  23. Binmore, Ken & Swierzbinski, Joe & Proulx, Chris, 2001. "Does Minimax Work? An Experimental Study," Economic Journal, Royal Economic Society, vol. 111(473), pages 445-464, July.
  24. Selten, Reinhard, 1998. "Features of experimentally observed bounded rationality," European Economic Review, Elsevier, vol. 42(3-5), pages 413-436, May.
  25. Binmore, Ken, 1988. "Modeling Rational Players: Part II," Economics and Philosophy, Cambridge University Press, vol. 4(01), pages 9-55, April.
  26. Ho, Teck-Hua & Camerer, Colin & Weigelt, Keith, 1998. "Iterated Dominance and Iterated Best Response in Experimental "p-Beauty Contests."," American Economic Review, American Economic Association, vol. 88(4), pages 947-969, September.
  27. Cooper,Russell, 1999. "Coordination Games," Cambridge Books, Cambridge University Press, number 9780521578967, October.
  28. Stahl, Dale O., 1998. "Is step-j thinking an arbitrary modelling restriction or a fact of human nature?," Journal of Economic Behavior & Organization, Elsevier, vol. 37(1), pages 33-51, September.
  29. Rapoport, Amnon & Amaldoss, Wilfred, 2000. "Mixed strategies and iterative elimination of strongly dominated strategies: an experimental investigation of states of knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 42(4), pages 483-521, August.
  30. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
  31. Dan Lovallo & Colin Camerer, 1999. "Overconfidence and Excess Entry: An Experimental Approach," American Economic Review, American Economic Association, vol. 89(1), pages 306-318, March.
  32. Rapoport, Amnon & Boebel, Richard B., 1992. "Mixed strategies in strictly competitive games: A further test of the minimax hypothesis," Games and Economic Behavior, Elsevier, vol. 4(2), pages 261-283, April.
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:oup:qjecon:v:119:y:2004:i:3:p:861-898.. 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: (Oxford University Press)

or (Christopher F. Baum)

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.