Hostname: page-component-7b9c58cd5d-9klzr Total loading time: 0 Render date: 2025-03-15T17:59:07.708Z Has data issue: false hasContentIssue false
  • English
  • Français

Relative versus Absolute Speed of Adjustment in Strategic Environments: Responder Behavior in Ultimatum Games

Published online by Cambridge University Press:  14 March 2025

David J. Cooper ,
Nick Feltovich ,
Alvin E. Roth  and
Rami Zwick
David J. Cooper
Affiliation:
Case Western Reserve University
Nick Feltovich
Affiliation:
University of Houston
Alvin E. Roth
Affiliation:
Harvard University
Rami Zwick
Affiliation:
Hong Kong University of Science and Technology
Get access Rights & Permissions [Opens in a new window]

Abstract

Learning models predict that the relative speed at which players in a game adjust their behavior has a critical influence on long term behavior. In an ultimatum game, the prediction is that proposers learn not to make small offers faster than responders learn not to reject them. We experimentally test whether relative speed of learning has the predicted effect, by manipulating the amount of experience accumulated by proposers and responders. The experiment allows the predicted learning by responders to be observed, for the first time.

Keywords

Game Theorylearningbargaining

JEL classification

C7: Game Theory and Bargaining Theory C9: Design of Experiments D83: Search • Learning • Information and Knowledge • Communication • Belief • Unawareness
Type
Research Article
Information
Experimental Economics , Volume 6 , Issue 2 , October 2003 , pp. 181 - 207
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

Blackburn, J.M. (1936). “Acquisition of Skill: An Analysis of Learning Curves.” IHRB Report No. 73.Google Scholar
Bolton, G. (1991). “A Comparative Model of Bargaining: Theory and Evidence.” American Economic Review. 81, 1096–1136.Google Scholar
Bolton, G.E. and Ockenfels, A. (1999). “ERC: A Theory of Equity, Reciprocity and Competition.” American Economic Review, forthcoming.Google Scholar
Bornstein, G., Erev, I., and Goren, H. (1994). Learning processes and reciprocity in intergroup conflicts. Journal of Conflict Resolution. 38, 690–707.CrossRefGoogle Scholar
Bornstein, G., Winter, E., and Goren, H. (1996). “Experimental Study of Repeated Team Games.” European Journal of Political Economy Volume 12, Issue 4, 17-December-1996.CrossRefGoogle Scholar
Cooper, D.J., Garvin, S., and Kagel, J.H. (1997). “Adaptive Learning versus Equilibrium Refinements in an Entry Limit Pricing Game.” Economic Journal. 107, 553–575.CrossRefGoogle Scholar
Cooper, D.J., Feltovich, N., Roth, A.E., and Zwick, R. (1999). “Relative versus Absolute Speed of Adjustment in Strategic Environments: Responder Behavior in Ultimatum Games.” Working Paper.Google Scholar
Cooper, D.J. and Stockman, C.K. (2002). “Fairness and Learning in a Step-Level Public Goods Game.” Games and Economic Behavior. 41, 26–45.CrossRefGoogle Scholar
Duffy, J. and Feltovich, N. (1999). “Does Observation of Others Affect Learning in Strategic Environments? An Experimental Study.” International Journal of Game Theory. 28, 131–152.CrossRefGoogle Scholar
Erev, I. (1998). “Signal Detection by Human Observers: A Cutoff Reinforcement Learning Model of Categorization Decisions Under Uncertainty. Psychological Review. 105, 280–298.CrossRefGoogle ScholarPubMed
Erev, I. and Rapoport, A. (1998). “Magic, Reinforcement Learning and Coordination in a Market Entry Game.” Games and Economic Behavior. 23, 146–175.CrossRefGoogle Scholar
Erev, I. and Roth, A.E. (1998). “Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria,” American Economic Review. 88(4), 848–881.Google Scholar
Erev, I., Roth, A.E., Slonim, R.L., and Barron, G. “Combining a Theoretical Prediction with Experimental Evidence.” Revised 2002.CrossRefGoogle Scholar
Fehr, E. and Schmidt, K.M. (1999). “A Theory of Fairness, Competition, and Cooperation.” Quarterly Journal of Economics. 114, 817–868.CrossRefGoogle Scholar
Feltovich, N. (2000). “Reinforcement-Based vs. Beliefs-Based Learning Models in Experimental Asymmetric- Information Games.” Econometrica. 68, 605–641.CrossRefGoogle Scholar
Forsythe, R., Horowitz, J., Savin, N.E., and Sefton, M. (1994). “Fairness in Simple Bargaining Experiments.” Games and Economic Behavior. 6, 347–369.CrossRefGoogle Scholar
Gale, J., Binmore, K., and Samuelson, L. (1995). “Learning to be Imperfect: The Ultimatum Game.” Games and Economic Behavior 8, 56–90.CrossRefGoogle Scholar
Güth, W., Schmittberger, R., and Schwarz, B. (1982). “An Experimental Analysis of Ultimatum Bargaining.” Journal of Economic Behavior and Organization. 3, 367–388.CrossRefGoogle Scholar
Harrison, G. and McCabe, K. (1996). “Expectations and Fairness in a Simple Bargaining Experiment.” International Journal of Game Theory. 25, 303–327.CrossRefGoogle Scholar
List, J. and Cherry, T. (2000). “Learning to Accept in Ultimatum Games: Evidence from an Experimental Design the Generates Low Offers.” Experimental Economics. 3, 11–30.CrossRefGoogle Scholar
Mookherjee, D. and Sopher, B. (1994). “Learning Behavior in an Experimental Matching Pennies Games.” Games and Economic Behavior. 7, 62–91.CrossRefGoogle Scholar
Mookherji, D. and Sopher, B. (1997). “Learning and Decision Costs in Experimental Constant Sum Games.” Games and Economic Behavior. 19(1), 97–132.CrossRefGoogle Scholar
Moulton, B. (1986). “Random Group Effects and the Prevision of Regression Estimates.” Journal of Econometrics. 32, 385–397.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
Ochs, J. and Roth, A.E. (1989). “An Experimental Study of Sequential Bargaining.” American Economic Review. 79, 355–384.Google Scholar
Rabin, M. (1993). “Incorporating Fairness into Game Theory and Economics.” American Economic Review. 83, 1281–1302.Google Scholar
Rapoport, A., Erev, I., Abraham, E.V., and Olson, D.E. (1997). “Randomization and Adaptive Learning in a Simplified Poker Game.” Organizational Behavior and Human Decision Processes. 69, 31–49.CrossRefGoogle Scholar
Rapoport, A., Seale, D., Erev, I., and Sundali, J.A. (1998). “Coordination Success in Market Entry Games: Tests of Equilibrium and Adaptive Learning Models.” Management Science. 44, 119–141.CrossRefGoogle Scholar
Roth, A.E. (1995). “Bargaining Experiments.” Handbook of Experimental Economics, J. Kagel and A.E. Roth (eds.). Princeton University Press, pp. 253–348.CrossRefGoogle Scholar
Roth, A.E. and Erev, I. (1995). “Learning in Extensive-Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term.” Games and Economic Behavior, Special Issue: Nobel Symposium. 8, 164212.Google Scholar
Roth, A.E., Prasnikar, V., Okuno-Fujiwara, M., and Zamir, S. (1991). “Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study.” American Economic Review. 81, 10681095.Google Scholar
Samuelson, L. (2001). “Introduction to the Evolution of Preferences.” Journal of Economic Theory. 97, 225–230.CrossRefGoogle Scholar
Sarin, R. and Vahid, F. (2001). “Predicting How People Play Games: A Simple Dynamic Model of Choice.” Games and Economic Behavior. 34, 104–122.CrossRefGoogle Scholar
Slonim, R. and Roth, A.E. (1998). “Learning in High Stakes Ultimatum Games: An Experiment in the Slovak Republic.” Econometrica. 66(3), 569–596.CrossRefGoogle Scholar
Tang, F.-F. (1995). “Anticipatory Learning in Two-Person Games: An Experimental Study.” Dissertation, University of Bonn.Google Scholar
Thorndike, E.L. (1898). Animal Intelligence: An Experimental Study of the Associative Processes in Animals. Psychological Monographs, 2.CrossRefGoogle Scholar
Van Huyck, J.B., Cook, J.P., and Battalio, R.C. (1994). “Selection Dynamics, Asymptotic Stability, and Adaptive Behavior.” Journal of Political Economy. 102, 975–1005.CrossRefGoogle Scholar