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No Switchbacks: Rethinking Aspiration-Based Dynamics in the Ultimatum Game

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  • Jeffrey Carpenter
  • Peter Matthews

Abstract

The stylized facts of ultimatum bargaining in the experimental lab are that offers tend to be near an equal split of the surplus and low, near perfect offers are routinely rejected. Bimmore et al (1995) use aspiration-based evolutionary dynamics to model the evolution of fair play in a binary choice version of this game, and show that incredible threats to reject low offers persist in equilibrium. We focus on two possible extensions of this analysis: (1) the model makes assumptions about agent motivations (aspiration levels) and the structure of the game (binary strategy space) that have not yet been tested experimentally, and (2) the standard dynamic is based on the problematic assumption that unhappy games who switch strategies may end up using the same strategy that was just rejected. To examine the implications of not allowing agents to “switch back” to their original strategy, we develop a “no switchback dynamic” and run a new, binary choice, experiment with induced aspirations. We find that the resulting dynamic predicts the evolution of play better than the standard dynamic and that aspirations are a significant motivator for our participants.

Suggested Citation

  • Jeffrey Carpenter & Peter Matthews, 2002. "No Switchbacks: Rethinking Aspiration-Based Dynamics in the Ultimatum Game," Middlebury College Working Paper Series 0218, Middlebury College, Department of Economics.
    • Handle: RePEc:mdl:mdlpap:0218
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    References listed on IDEAS

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    1. Karandikar, Rajeeva & Mookherjee, Dilip & Ray, Debraj & Vega-Redondo, Fernando, 1998. "Evolving Aspirations and Cooperation," Journal of Economic Theory, Elsevier, vol. 80(2), pages 292-331, June.
    2. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
    3. Van Huyck, John & Battalio, Raymond & Mathur, Sondip & Van Huyck, Patsy & Ortmann, Andreas, 1995. "On the Origin of Convention: Evidence from Symmetric Bargaining Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 187-212.
    4. Vesna Prasnikar & Alvin E. Roth, 1992. "Considerations of Fairness and Strategy: Experimental Data from Sequential Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 865-888.
    5. Jonathan Bendor & Dilip Mookherjee & Debraj Ray, 2001. "ASPIRATION-BASED REINFORCEMENT LEARNING IN REPEATED INTERACTION GAMES: Aspiration-Based Reinforcement Learning in Repeated Games AN OVERVIEW," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 159-174.
    6. Jeffrey Carpenter, 2002. "Bargaining Outcomes as the Result of Coordinated Expectations: An Experimental Study of Sequential Bargaining," Middlebury College Working Paper Series 0204, Middlebury College, Department of Economics.
    7. Jeffrey P. Carpenter, 2003. "Bargaining Outcomes as the Result of Coordinated Expectations," Journal of Conflict Resolution, Peace Science Society (International), vol. 47(2), pages 119-139, April.
    8. Van Huyck, John B & Cook, Joseph P & Battalio, Raymond C, 1994. "Selection Dynamics, Asymptotic Stability, and Adaptive Behavior," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 975-1005, October.
    9. Bolton Gary E. & Zwick Rami, 1995. "Anonymity versus Punishment in Ultimatum Bargaining," Games and Economic Behavior, Elsevier, vol. 10(1), pages 95-121, July.
    10. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
    11. Guth, Werner & Schmittberger, Rolf & Schwarze, Bernd, 1982. "An experimental analysis of ultimatum bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 367-388, December.
    12. Bendor Jonathan & Mookherjee Dilip & Ray Debraj, 2001. "Reinforcement Learning in Repeated Interaction Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, March.
    13. Friedman, Daniel, 1996. "Equilibrium in Evolutionary Games: Some Experimental Results," Economic Journal, Royal Economic Society, vol. 106(434), pages 1-25, January.
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    Cited by:

    1. Jeffrey Carpenter & Peter Matthews, 2002. "Social Reciprocity," Middlebury College Working Paper Series 0229, Middlebury College, Department of Economics.
    2. Jeffrey P. Carpenter & Peter Hans Matthews, 2013. "Crying Over Spilt Milk: Sunk Costs, Fairness Norms and the Hold-up Problem," Studies in Microeconomics, , vol. 1(2), pages 113-129, December.
    3. Benchekroun, Hassan & Long, Ngo Van, 2008. "The build-up of cooperative behavior among non-cooperative selfish agents," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 239-252, July.
    4. Carpenter, Jeffrey P., 2004. "When in Rome: conformity and the provision of public goods," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 33(4), pages 395-408, September.
    5. Carpenter, Jeffrey P., 2003. "Is fairness used instrumentally? Evidence from sequential bargaining," Journal of Economic Psychology, Elsevier, vol. 24(4), pages 467-489, August.

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    More about this item

    Keywords

    ultimatum game; learning; aspirations; switchbacks; replicator dynamics;
    All these keywords.

    JEL classification:

    • 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

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