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What Does it Take to Eliminate the use of a Strategy Strictly Dominated by a Mixture?

Published online by Cambridge University Press:  14 March 2025

John Van Huyck*
Affiliation:
Texas A&M University
Frederick Rankin
Affiliation:
Washington University
Raymond Battalio
Affiliation:
Texas A&M University

Abstract

This paper reports an experiment to determine whether subjects will learn to stop using a strictly dominated strategy that can be an above average reply. It is difficult to find an experimental design that eliminates the play of the strictly dominated strategy completely. The least effective treatment used money to motivate behavior directly. The most effective treatment used a binary-lottery with money prizes to induce preferences, but even this treatment required giving subjects plenty of experience. Doing so reduced the play of the strictly dominated strategy to around 10 percent by the end of a session. There is no evidence for the explosive cycling needed to make the strictly dominated strategy an above average reply.

Type
Research Article
Copyright
Copyright © 1999 Economic Science Association

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Footnotes

1

Related research available at http://erl.tamu.edu/

References

Anderson, Simon, Goeree, Jacob, and Holt, Charles. (1996). “Minimum-effort Coordination Games: An Equilibrium Analysis of Bounded Rationality” laser-script.Google Scholar
Binmore, Ken, Proulx, Chris, and Swierzbinski, J. (1997). “Does Minimax Work? an experimental study,” laserscript.Google Scholar
Brown, J. and Rosenthal, R. (1990). “Testing the Minimax Hypothesis: A Re-examination of O’Neill's Experiment.” Econometrica. 58, 10651081.CrossRefGoogle Scholar
Cabrales, Antonio, and Sobel, Joel. (1992). “On the Limit Points of Discrete Selection Dynamics.” Journal of Economic Theory. 57(3), 407419.CrossRefGoogle Scholar
Cooper, Russell, DeJong, Douglas, Forsythe, Robert, and Ross, Thomas. (1996). “Cooperation without Reputation: Experimental Evidence from Prisoner's Dilemma Games.” Games and Economic Behavior 12(2), 187218.CrossRefGoogle Scholar
Crawford, Vincent P. (1991). “An ‘Evolutionary’ Interpretation of Van Huyck, Battalio, and Beil's Experimental Results on Coordination.” Games and Economic Behavior. 3, 2560.CrossRefGoogle Scholar
Crawford, Vincent P. (1993). “Introduction.” Games and Economic Behavior. 5(3), 315319.Google Scholar
Dekel, Eddie and Scotchmer, Susan. (1992). ”On the Evolution of Optimizing Behavior.” Journal of Economic Theory. 57, 392406.CrossRefGoogle Scholar
Friedman, Daniel. (1991). “Evolutionary Games in Economics.” Econometrica. 59(3), 637666.CrossRefGoogle Scholar
Friedman, Daniel. (1996). “Equilibrium in Evolutionary Games: Some Experimental Results.” Economic Journal. 106(434), 125.CrossRefGoogle Scholar
Fudenberg, Drew and Kreps, David M. (1993). “Learning Mixed Equilibria.” Games and Economic Behavior. 5(3), 320367.CrossRefGoogle Scholar
Hofbauer, Josef and Sigmund, Karl. (1988). The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection. Cambridge, UK: Cambridge University Press.Google Scholar
Jordan, J. S. (1993). “Three Problems in Learning Mixed-Strategy Nash Equilibria.” Games and Economic Behavior. 5(3), 368386.CrossRefGoogle Scholar
Milgrom, Paul and Roberts, John. (1991). “Adaptive and Sophisticated Learning in Normal Form Games.” Games and Economic Behavior. 3, 82100.CrossRefGoogle Scholar
McKelvey, Richard D. and Palfrey, Thomas R. (1995). “Quantal Response Equilibria for Normal Form Games.” Games and Economic Behavior. 638.CrossRefGoogle Scholar
McKelvey, Richard, Palfrey, Thomas, and Weber, Roberto. (1997). “The Effects of Payoff Magnitude and Heterogeneity on Behavior in 2 × 2 Games with Unique Mixed Strategy Equilibria,” laser-script.Google Scholar
O’Neill, Barry. (1987). “Nonmetric Test of the Minimax Theory of Two-person Zerosum Games.” Proceedings of the National Academy of Sciences. 84, 21062109.CrossRefGoogle ScholarPubMed
Offerman, Theo, Schram, Arthur, and Sonnemans, Joep. (1998). “Quantal Response Models in Step-Level Public Goods Games.” European Journal of Political Economy. 14(1), 89100.CrossRefGoogle Scholar
Prasnikar, Vesna. (1993). “Binary Lottery Payoffs: Do they control risk aversion?” laser-script.Google Scholar
Rapoport, Amnon and Boebel, Richard. (1992). “Mixed Strategies in Strictly Competitive Games: A Further Test of the Minimax Hypothesis.” Games and Economic Behavior. 4(2), 261283.CrossRefGoogle Scholar
Rapoport, Anatol, Guyer, Melvin, and Gordon, David. (1976). The 2 × 2 Game, Ann Arbor, MI: University of Michigan Press.Google Scholar
Rietz, Thomas. (1993). “Implementing and Testing Risk-Preference-Induction Mechanisms in Experimental Sealed-bid Auctions.” Journal of Risk and Uncertainty. 7(2), 199213.CrossRefGoogle Scholar
Roth, Alvin E. (1995). “Introduction” In Handbook of Experimental Economics, (eds.) Kagel, and Roth, , Princeton, NJ: Princeton University Press.Google Scholar
Roth, Alvin E. and Malouf, M. (1979). “Game-Theoretic Models and the Role of Information in Bargaining.” Psychological Review. 574-594.CrossRefGoogle Scholar
Selten, Reinhard, Sadrieh, Abdolkarim, and Abbink, Klaus. (1995). “Money Does Not Induce Risk Neutral Behavior, But Binary Lotteries Do Even Worse.” laser-script.Google Scholar
Shachat, Jason. (1996). “Mixed Strategy Play and the Minimax Hypothesis,” laser-script.Google Scholar
Van Huyck, J., Battalio, R., Mathur, S., Ortmann, A., and Van Huyck, P (1995). “On the Origin of Convention: Evidence from Symmetric Bargaining Games.” International Journal of Game Theory. 24(2), 187212.CrossRefGoogle Scholar
Van Huyck, John, Battalio, Raymond, and Rankin, Frederick. (1997). “On the Origin of Convention: Evidence From Coordination Games.” The Economic Journal. 107(442), 576597.CrossRefGoogle Scholar
Weibull, Jorgen W. (1995). Evolutionary Game Theory. Cambridge, MA: The MIT Press.Google Scholar
Weissing, F. (1991). “Evolutionary stability and dynamic stability in a class of evolutionary normal form games,” In Games Equilibrium Models. I Evolution and Game Dynamics. Berlin/New York: Springer-Verlag, pp. 2997.CrossRefGoogle Scholar
Wooders, John and Shachat, Jason M. (1997). “On the Irrelevance of Risk Attitudes in Repeated Two-Outcome Games,” laser-script.Google Scholar