Hostname: page-component-5cf477f64f-xc2pj Total loading time: 0 Render date: 2025-03-30T06:33:53.116Z Has data issue: false hasContentIssue false
  • English
  • Français

Reinforcement and Directional Learning in the Ultimatum Game with Responder Competition

Published online by Cambridge University Press:  14 March 2025

Brit Grosskopf
Brit Grosskopf*
Affiliation:
Harvard Business School, 174 Baker Library, Soldier's Field Road, Boston, MA 02163, USA
*
email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Demands in the Ultimatum Game in its traditional form with one proposer and one responder are compared with demands in an Ultimatum Game with responder competition. In this modified form one proposer faces three responders who can accept or reject the split of the pie. Initial demands in both ultimatum games are quite similar, however in the course of the experiment, demands in the ultimatum game with responder competition are significantly higher than in the traditional case with repeated random matching. Individual round-to-round changes of choices that are consistent with directional learning are the driving forces behind the differences between the two learning curves and cannot be tracked by an adjustment process in response to accumulated reinforcements. The importance of combining reinforcement and directional learning is addressed. Moreover, learning transfer between the two ultimatum games is analyzed.

Keywords

ultimatum gamecompetitionreinforcement learningdirectional learninglearning transfer

JEL classification

C91: Laboratory, Individual Behavior D83: Search • Learning • Information and Knowledge • Communication • Belief • Unawareness C72: Noncooperative Games
Type
Research Article
Information
Experimental Economics , Volume 6 , Issue 2 , October 2003 , pp. 141 - 158
Copyright
Copyright © 2003 Economic Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbink, K., Bolton, G.E., Sadrieh, A., and Tang, F.-F. (2001). “Adaptive Learning versus Punishment in Ultimatum Bargaining.” Games and Economic Behavior. 37(1), 1–25.CrossRefGoogle Scholar
Barron, G. and Erev, I. (2001). “On Adaptation, Maximization, and Reinforcement Learning Among Cognitive Strategies.” Mimeo, Technion, Haifa.Google Scholar
Bolton, G.E. (1998). “Strong and Weak Equity Effects: Evidence, Significance and Origins.” In Budescu, D., I. E. and Zwick, R. (eds.), Games and Human Behavior, Essays in Honor of Amnon Rapoport, Hillsdale, NJ.Google Scholar
Bolton, G.E. and Ockenfels, A. (2000). “ERC—A Theory of Equity, Reciprocity, and Competition.” American Economic Review. 90(1), 166–193.CrossRefGoogle Scholar
Bolton, G.E. and Zwick, R. (1995). “Anonymity versus Punishment in Ultimatum Bargaining.” Games and Economic Behavior. 10, 95–121.CrossRefGoogle Scholar
Cachon, G.P. and Camerer, C. (1996). “The Sunk Cost Fallacy, Forward Induction and Behavior in Coordination Games.” Quarterly Journal of Economics. 111, 165–194.CrossRefGoogle Scholar
Camerer, C.F. and Ho, T.H. (1999). “Experience—Weighted Attraction Learning in Games: A Unifying Approach.”. Econometrica. 67, 827–874.CrossRefGoogle Scholar
Camerer, C.F., Ho, T.H., and Wang, X. (2002). “Individual Differences in EWA Learning with Partial Payoff Information.” Mimeo.Google Scholar
Cason, T. and Friedman, D. (1997). “Price Formation in Single Call Markets.” Econometrica. 65(2), 311–345.CrossRefGoogle Scholar
Crawford, V.P. (1995). “Adaptive Dynamics in Coordination Games.” Econometrica. 63, 103–143.CrossRefGoogle Scholar
Duffy, J. and Nagel, R. (1997). “On the Robustness of Behavior in Experimental Beauty-Contest Games.” Economic Journal. 107, 1684–1700.CrossRefGoogle Scholar
Erev, I. and Rapoport, A. (1998). “Coordination, ‘Magic,’ and Reinforcement Learning in a Market Entry Game.” Games and Economic Behavior. 23, 146–175.CrossRefGoogle Scholar
Erev, I. and Roth, A. (Unpublished). “Adaptation and Imitation in Experimental Games.” Technical Report.Google Scholar
Erev, I. and Roth, A.E. (1998a). “Predicting How People Play Games: Reinforcing Learning in Experimental Games with Unique, Mixed Strategy Equilibria.” American Economic Review. 88(4), 848–881.Google Scholar
Erev, I. and Roth, A.E. (1998b). “On the Role of Reinforcement Learning.” In Budescu, D., I.E. and Zwick, R. (eds.), Games and Human Behavior, Essays in Honor of Amnon Rapoport, Hillsdale, NJ.Google Scholar
Fehr, E. and Schmidt, K. (1999). “A Theory of Fairness, Competition and Cooperation.” Quarterly Journal of Economics. 114, 817–868.CrossRefGoogle Scholar
Gale, J., Binmore, K.G., and Samuelson, L. (1995). “Learning to be Imperfect: The Ultimatum Game.” Games and Economic Behavior. 8, 56–90.CrossRefGoogle Scholar
Gick, M.L. and Holyoak, K.J. (1980). “Analogical Problem Solving.” Cognitive Psychology. 12, 306–355.CrossRefGoogle Scholar
Gick, M.L. and Holyoak, K.J. (1983). “Schema Induction and Analogical Transfer.” Cognitive Psychology. 15, 1–38.CrossRefGoogle Scholar
Glassnapp, D. and Poggio, J. (1985). Essentials of Statistical Analysis for the Behavioral Sciences. Columbus, OH: Merrill.Google Scholar
Grosskopf, B. (2001). “Merging Reinforcement and Directional Learning—A Generalized Model.” Mimeo.Google Scholar
Grosskopf, B., Erev, I., and Yechiam, E. (2001). “Foregone with the Wind.” Mimeo.Google Scholar
Güth, W., Marchand, N., and Rulliere, J.-L. (1997). “On the Reliability of Reciprocal Fairness—An Experimental Study.” Mimeo.Google Scholar
Güth, W., Schmittberger, R., and Schwarze, B. (1982). “An Experimental Analysis of Ultimatum Bargaining.” Journal of Economic Behavior and Organization. 3, 367–388.CrossRefGoogle Scholar
Ho, T., Camerer, C., and Weigelt, K. (1998). “Iterated Dominance and Iterated Best Response in Experimental p-Beauty Contests.” American Economic Review. 88(4), 947–969.Google Scholar
Huck, S., Normann, H.-T., and Oechssler, J. (1999). “Learningin Cournot-Oligopoly—An Experiment.” Economic Journal. 109(454), C80–95.CrossRefGoogle Scholar
Kagel, J. and Levin, D. (1999). “Common Value Auctions with Insider Information.” Econometrica. 67(5), 12191238.CrossRefGoogle Scholar
Kimble, G.A. (1961). Hilgard and Marquis’ Conditioning and Learning. Englewood Cliffs, Prentice Hall.Google Scholar
Kuon, B. (1994). Two-person Bargaining Experiments with Incomplete Information. Springer Lecture Notes in Economics and Mathematical Systems (No. 412). Berlin, Heidelberg, New York: Springer.CrossRefGoogle Scholar
Messick, D.M., Moore, D.A., and Bazerman, M.H. (1997). “Ultimatum Bargaining with a Group: Underestimating the Importance of the Decision Rule.” Organizational Behavior and Human Decision Processes. 69, 87–101.CrossRefGoogle Scholar
Mitzkewitz, M. and Nagel, R. (1993). “Experimental Results on Ultimatum Games with Incomplete Information.” International Journal of Game Theory. 22, 171–198.CrossRefGoogle Scholar
Mookherjee, D. and Sopher, B. (1997). “Learning and Decision Costs in Experimental Constant Sum Games.” Games and Economic Behavior. 19, 97–132.CrossRefGoogle Scholar
Nagel, R. and Tang, F.F. (1998). “Experimental Results on the Centipede Game in Normal Form: An Investigation on Learning.” Journal of Mathematical Psychology. 42, 356–384.CrossRefGoogle ScholarPubMed
Nagel, R. and Vriend, N. (1999). “An Experimental Study of Adaptive Behavior in an Oligopolistic Market Game.” Journal of Evolutionary Economics. 9, 27–65.CrossRefGoogle Scholar
Perkins, D.N. and Salomon, G. (1988). “Teaching for Transfer.” Educational Leadership. 46, 22–32.Google Scholar
Roth, A. and Erev, I. (1995). “Learning in Extensive Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term.” Games and Economics Behavior. 8, 164–212.CrossRefGoogle Scholar
Roth, A.E. (1995). “Bargaining Experiments.” In Kagel, J. and Roth, A.E. (eds.), Handbook of Experimental Economics, Princeton University Press.Google Scholar
Salomon, G. and Perkins, D.N. (1989). “Rocky Roads to Transfer: Rethinking Mechanisms of a Neglected Phenomenon.” Education Psychologist. 24, 113–142.CrossRefGoogle Scholar
Selten, R. and Buchta, J. (1998). “Experimental Sealed Bid First Price Auction with Directly Observed Bid Functions.” In Budescu, D., I.E. and Zwick, R. (eds.), Games and Human Behavior, Essays in Honor of Amnon Rapoport, Hillsdale, NJ.Google Scholar
Selten, R. and Stoecker, R. (1986). “End Behavior in Sequences of Finite Prisoner's Dilemma Supergames: A Learning Theory Approach.” Journal of Economic Behavior and Organization. 7(1), 47–70.CrossRefGoogle Scholar
Slonim, R. and Roth, A.E. (1998). “Financial Incentives and Learning in Ultimatum and Market Games: An Experiment in the Slovak Republic.” Econometrica. 66(3), 569–596.CrossRefGoogle Scholar