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

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  • Jeffrey Carpenter
  • Peter Hans Matthews

Abstract

Aspiration-based evolutionary dynamics have recently been used to model the evolution of fair play in the ultimatum game showing that incredible threats to reject low offers persist in equilibrium. We focus on two extensions of this analysis: we experimentally test whether assumptions about agent motivations (aspiration levels) and the structure of the game (binary strategy space) reflect actual play, and we examine the problematic assumption embedded in the standard replicator dynamic that unhappy agents who switch strategies may return to a rejected strategy without exploring other options. We find that the resulting "no switchback" dynamic predicts the evolution of play better than the standard dynamic and that aspirations are a significant motivator for our participants. In the process, we also construct and analyze a variant of the ultimatum game in which players can adopt conditional (on their induced aspirations) stategies.

Suggested Citation

  • Jeffrey Carpenter & Peter Hans Matthews, 2003. "No Switchbacks: Rethinking Aspiration-Based Dynamics in the Ultimatum Game," Middlebury College Working Paper Series 0218r, Middlebury College, Department of Economics.
    • Handle: RePEc:mdl:mdlpap:0218r
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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.
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    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.
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    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.
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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; replicator dynamics; experiment;
    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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