How to Play 3x3-Games A Strategy Method Experiment
AbstractWe 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.
Download InfoIf 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.
Bibliographic InfoPaper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse3_2001.
Date of creation: Nov 2000
Date of revision:
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: http://www.bgse.uni-bonn.de
2-person games; experimental economics;
Other versions of this item:
- Selten, Reinhard & Abbink, Klaus & Buchta, Joachim & Sadrieh, Abdolkarim, 2003. "How to play (3 x 3)-games.: A strategy method experiment," Games and Economic Behavior, Elsevier, vol. 45(1), pages 19-37, October.
- Selten, R. & Abbink, K. & Buchta, J. & Sadrieh, A., 2002. "How to Play 3x3 Games: A Strategy Method Experiment," Discussion Paper 2002-39, Tilburg University, Center for Economic Research.
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
- C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
- C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
This paper has been announced in the following NEP Reports:
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.:
- Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
- 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.
- Dale O. Stahl & Paul W. Wilson, 2010. "On Players' Models of Other Players: Theory and Experimental Evidence," Levine's Working Paper Archive 542, David K. Levine.
- Claudia Keser & Roy Gardner, 1999.
"Strategic behavior of experienced subjects in a common pool resource game,"
International Journal of Game Theory,
Springer, vol. 28(2), pages 241-252.
- 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.
- Selten,Reinhard & Mitzkewitz,Michael & Uhlich,Gerald, .
"Duopoly strategies programmed by experienced players,"
Discussion Paper Serie B
106, University of Bonn, Germany.
- Reinhard Selten & Michael Mitzkewitz & Gerald R. Uhlich, 1997. "Duopoly Strategies Programmed by Experienced Players," Econometrica, Econometric Society, vol. 65(3), pages 517-556, May.
- Nagel, Rosemarie, 1993. "Experimental Results on Interactive Competitive Guessing," Discussion Paper Serie B 236, University of Bonn, Germany.
- 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.
- Steffen Huck & Joerg Oechssler, 1999.
"Informational cascades in the laboratory: Do they occur for the right reasons?,"
- Huck, Steffen & Oechssler, Jorg, 2000. "Informational cascades in the laboratory: Do they occur for the right reasons?," Journal of Economic Psychology, Elsevier, vol. 21(6), pages 661-671, December.
- Staffiero, Gianandrea, 2006. "Helping the meaner, hurting the nicer: The contribution versus distribution game," IESE Research Papers D/652, IESE Business School.
- Pittel, Karen & Rübbelke, Dirk T. G., 2012.
"Transitions in the negotiations on climate change: From prisoner’s dilemma to chicken and beyond,"
Munich Reprints in Economics
19343, University of Munich, Department of Economics.
- Karen Pittel & Dirk Rübbelke, 2012. "Transitions in the negotiations on climate change: from prisoner’s dilemma to chicken and beyond," International Environmental Agreements: Politics, Law and Economics, Springer, vol. 12(1), pages 23-39, March.
- Roy Gardner, 2007. "Michael Bacharach, Beyond Individual Choice: Teams and Frames in Game Theory. Princeton, NJ: Princeton University Press, 2006. xxiii + 214 pages. USD 35.00 (cloth)," Public Choice, Springer, vol. 130(3), pages 495-497, March.
- Grimm, Veronika & Mengel, Friederike, 2012.
"An experiment on learning in a multiple games environment,"
Journal of Economic Theory,
Elsevier, vol. 147(6), pages 2220-2259.
- Grimm, Veronika & Mengel, Friederike, 2009. "An Experiment on Learning in a Multiple Games Environment," Research Memorandum 007, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Olivier Armantier, 2001. "Does Wealth Affect Fairness Considerations?," Department of Economics Working Papers 01-05, Stony Brook University, Department of Economics.
- Boone, Jan & Sadrieh, Abdolkarim & van Ours, Jan C., 2004.
"Experiments on Unemployment Benefit Sanctions and Job Search Behavior,"
IZA Discussion Papers
1000, Institute for the Study of Labor (IZA).
- Boone, Jan & Sadrieh, Abdolkarim & van Ours, Jan C., 2009. "Experiments on unemployment benefit sanctions and job search behavior," European Economic Review, Elsevier, vol. 53(8), pages 937-951, November.
- Boone, Jan & Sadrieh, Abdolkarim & van Ours, Jan C, 2004. "Experiments on Unemployment Benefit Sanctions and Job Search Behaviour," CEPR Discussion Papers 4298, C.E.P.R. Discussion Papers.
- Boone, J. & Sadrieh, A. & Ours, J.C. van, 2004. "Experiments on Unemployment Benefit Sanctions and Job Search Behavior," Discussion Paper 2004-8, Tilburg University, Center for Economic Research.
- Stahl, Dale O. & Haruvy, Ernan, 2008. "Level-n bounded rationality and dominated strategies in normal-form games," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 226-232, May.
- Spiwoks, Markus & Bizer, Kilian & Hein, Oliver, 2008. "Informational cascades: A mirage?," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 193-199, July.
- Olivier Armantier, 2006.
"Do Wealth Differences Affect Fairness Considerations?,"
CIRANO Working Papers
- Olivier Armantier, 2006. "Do Wealth Differences Affect Fairness Considerations?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 391-429, 05.
- Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.
- Annamaria Nese & Arturo Palomba & Patrizia Sbriglia & Maurizio Scudiero, 2013. "Third party punishment and criminal behavior: an experiment with the Italian Camorra prison inmates," Economics Bulletin, AccessEcon, vol. 33(3), pages 1875-1884.
- Jordi Brandts & Gary Charness, 2011. "The strategy versus the direct-response method: a first survey of experimental comparisons," Experimental Economics, Springer, vol. 14(3), pages 375-398, September.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (BGSE Office).
If references are entirely missing, you can add them using this form.