IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

How to Play 3x3-Games A Strategy Method Experiment

  • Reinhard Selten
  • Klaus Abbink
  • Joachim Buchta
  • Abdolkarim Sadrieh

We report an experiment that uses the strategy method (Selten 1967) to elicit subjects' general strategy for playing any 2-person 3x3-game with integer payoffs between 0 and 99. Each two subjects' strategies play 500000 games in each of the 5 tournaments. For games with pure strategy equilibria (ca. 80%), the frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, in which there is equilibrium play in 98% of all games with only one pure equilibrium. In games with more than one pure equilibrium, a tendency towards the selection of the one with the maximum joint payoff is observed. For games without pure equilibria, subjects’ strategies do not search for mixed equilibria. The strategy programs are based on much simpler strategic concepts combined in various ways. The simplest one is MAP, maximal average payoff, the strategy which maximizes the sum of the three payoffs obtainable against the possible choices of the other player. BR-MAP, the best reply to MAP, and BR-BR-MAP, the best reply to BR-MAP, are also important ingredients of the strategy programs. Together these three form a hierarchy to which we refer to as the best-reply cascade.

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: no

Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse3_2001.

in new window

Length: 26
Date of creation: Nov 2000
Date of revision:
Handle: RePEc:bon:bonedp:bgse3_2001
Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
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. Keser, C. & Gardner, R., 1994. "Strategic Behavior of Experienced Subjects in a Common Pool Resource Game," Papers 94-009, Indiana - Center for Econometric Model Research.
  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, June.
  3. Nagel, Rosemarie, 1993. "Experimental Results on Interactive Competitive Guessing," Discussion Paper Serie B 236, University of Bonn, Germany.
  4. Stahl Dale O., 1993. "Evolution of Smartn Players," Games and Economic Behavior, Elsevier, vol. 5(4), pages 604-617, October.
  5. Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
  6. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
  7. Stahl Dale O. & Wilson Paul W., 1995. "On Players' Models of Other Players: Theory and Experimental Evidence," Games and Economic Behavior, Elsevier, vol. 10(1), pages 218-254, July.
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:bon:bonedp:bgse3_2001. 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: (BGSE Office)

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.