Cooperation in Single Play, Two-Person Extensive form Games between Anonymously Matched Players

  • Kevin McCabe
  • Mary Rigdon
  • Vernon Smith


Experimentalists have long observed that many subjects in two-person extensive form games choose cooperative strategies even when they will be played only once matched with another person whose identity will never be revealed to them.1 This phenomenon has been observed most prominently, and replicated many times, in the large literature on ultimatum (and dictator) games, beginning with Güth, Schmittberger and Schwartz (1982). In the ultimatum game two anonymously paired subjects split k units of money. Player 1 proposes a split of x for Player 2 and k−x for Player 1. If Player 2 accepts, the money is split as proposed; if rejected, each gets zero. The modal outcome in these experiments is for Player 1 to offer half of the pie represented by k units of money; the mean offer is about 0.47k. Players 2 rarely reject offers as high as x = 0.4k and regularly reject offers of 0.1k, 0.2k and even 0.3k, where k = $10 2. These results are little changed when the stakes are greatly increased to k = $100 (Hoffutan, McCabe and Smith, 1996). Yet game theory predicts that Player 1 will offer the minimum unit of account, say $1, when k consists of 10 one-dollar bills, and Player 2 will accept.


Ultimatum Game Dictator Game Trust Game Inequity Aversion Single Play 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Berg, Joyce, John Dickhaut, and Kevin McCabe (1995). “Trust, Reciprocity and Social History.” Games and Economic Behavior 10, 122–42.CrossRefGoogle Scholar
  2. Bolton, Gary, and Axel Ockenfels (2000). “ERC: A Theory of Equity, Reciprocity, and Competition.” American Economic Review 90, 166–93.CrossRefGoogle Scholar
  3. Bolton, Gary, and Rami Zwick (1998). “Anonymity versus Punishment in Ultimatum Bargaining.” Games and Economic Behavior 10, 95–121.CrossRefGoogle Scholar
  4. Brown, Donald E. (1991). Human Universals. NY: McGraw-Hill.Google Scholar
  5. Burnham, Terence (1998). “Engineering Altruism: An Experimental Investigation of Anonymity Gift Giving.” Manuscript, Kennedy School of Government, Harvard University, Cambridge, MA.Google Scholar
  6. Burnham, Terence, Kevin McCabe, and Vernon Smith (2000). “Friend-or-Foe Intentionality Priming in an Extensive Form Trust Game.” Journal of Economic Behavior and Organization 1244, 1–17.Google Scholar
  7. Coricelli, Georgio, Kevin McCabe, and Vernon Smith (2000). “Theory-of-Mind Mechanism in Personal Exchange.” Proceedings 13th Annual Toyota Conference on Affective Minds.Google Scholar
  8. Cosmides, Leda (1985). “The Logic of Social Exchange: Has Natural Selection Shaped How Human Reason?” Cognition 31, 187–276.CrossRefGoogle Scholar
  9. Cox, James C. (1999). “Trust Reciprocity and Other-Regarding Preferences of Individuals and Groups.” Department of Economics and Economic Science Laboratory, University of Arizona.Google Scholar
  10. Deck, Cary (2000). “A Test of Game Theoretic and Behavioral Models of Play in Exchange and Insurance Environments.” Economic Science Laboratory, University of Arizona. Eckel, Catherine, and Philip Grossman (1996). “Altruism in Anonymous Dictator Games. ” Games and Economic Behavior 16, 181–91.Google Scholar
  11. Fehr, Ernst, and Klaus M. Schmidt (1999). “A Theory of Fairness, Competition, and Cooperation.” Quarterly Journal of Economics 114, 817–68.CrossRefGoogle Scholar
  12. Forsythe, Robert, Joel Horwitz, N. E. Savin, and Martin Sefton (1994). “Fairness in Simple Bargaining Experiments.” Games and Economic Behavior 6, 347–69.CrossRefGoogle Scholar
  13. Gouldner, Alvin W. (1960). “The Norm of Reciprocity.” American Sociological Review 25, 161–78.CrossRefGoogle Scholar
  14. Gunnthorsdottir, Anna, Kevin McCabe, and Vernon Smith (1999). “Using the Machiavellianism Instrument to Predict Trustworthiness in a Bargaining Game:’Google Scholar
  15. Güth, W, R. Schmittberger, and V. Schwartz (1982). “An Experimental Analysis of Ultimatum Bargaining.” Journal of Economic Behavior and Organization 3, 367–88.CrossRefGoogle Scholar
  16. Harsanyi, John (1967). “Games with Incomplete Information Played by ”Bayesian“ Players (Part I).” Management Science 14, 159–82.CrossRefGoogle Scholar
  17. Hoffman, Elizabeth, Kevin McCabe, Keith Shachat, and Vernon Smith (1994). “Preferences, Property Rights and Anonymity in Bargaining Games?’ Games and Economic Behavior 7, 346–80.CrossRefGoogle Scholar
  18. Hoffman, Elizabeth, Kevin McCabe, and Vernon Smith (1996). “Social Distance of Other-Google Scholar
  19. Regarding Behavior in Dictator Games.“ American Economic Review 86, 653–60. Hoffman, Elizabeth, and Matthew Spitzer (1982). ”The Coase Theorem: Some Experimental Tests.“ Journal of Law and Economics 25, 73–98.Google Scholar
  20. Hoffman, Elizabeth (1985). `Entitlements, Rights and Fairness.“ Journal of Legal Studies 14, 259–97.CrossRefGoogle Scholar
  21. Hume, David (1886). A Treatise of Human Nature. Vol. 2, edited by T. H. Green and T. H. Grose, 235. London: Longmans, Green.Google Scholar
  22. Kagel, John, and Alvin Roth (1995). The Handbook of Experimental Economics. Princeton: Princeton University Press.Google Scholar
  23. McCabe, Kevin, Stephen Rassenti, and Vernon Smith (1996). “Game Theory and Reciprocity in Some Extensive Form Experimental Games.” Proceedings of the National Academy of Sciences 93, 13421–8.CrossRefGoogle Scholar
  24. McCabe, Kevin, Mary Rigdon, and Vernon Smith (2000). “Positive Reciprocity and Intentions in Trust Games” Working Paper, University of Arizona.Google Scholar
  25. McCabe, Kevin, Vernon Smith, and Michael LePore (2000). “Intentionality Detection and ”Mindreading“: Why Does Game Form Matter.” Proceedings of the National Academy of Sciences 97, 4404–9.CrossRefGoogle Scholar
  26. Rabin, Matthew (1993). “Incorporating Fairness into Game Theory and Economics.” American Economic Review 83, 1281–302.Google Scholar
  27. Rapoport, Amnon (1997). “Order of Play in Strategically Equivalent Games in Extensive Form.” International Journal of Game Theory 26, 113–36.CrossRefGoogle Scholar
  28. Roth, Alvin E., Vesna Prasnikar, Masahiro Okuno-Fujiwara, and Shmuel Zamir (1991). `Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh and Tokyo.“ American Economic Review 81, 1068–95.Google Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Kevin McCabe
    • 1
  • Mary Rigdon
    • 1
  • Vernon Smith
    • 1
  1. 1.George Mason UniversityUSA

Personalised recommendations