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Sampling Dynamics of a Symmetric Ultimatum Game

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  • Jacek Miękisz
  • Michał Ramsza

Abstract

We propose a dynamic three-strategy symmetric model of the Ultimatum Game with players using a sampling procedure. We allow an intermediate strategy, interpreted as a social norm, to evolve in time according to beliefs of players about an average offer. We show that a social norm converges to a self-consistent offer of about 15 % in the unique globally asymptotically stable equilibrium of our model. Copyright The Author(s) 2013

Suggested Citation

  • Jacek Miękisz & Michał Ramsza, 2013. "Sampling Dynamics of a Symmetric Ultimatum Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 374-386, September.
    • Handle: RePEc:spr:dyngam:v:3:y:2013:i:3:p:374-386
    DOI: 10.1007/s13235-012-0064-5
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    References listed on IDEAS

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    1. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
    2. Jacek Miękisz & Michał Ramsza, 2012. "Replicator Dynamics of Symmetric Ultimatum Game," Dynamic Games and Applications, Springer, vol. 2(2), pages 258-268, June.
    3. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
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    5. Iris Bohnet & Richard Zeckhauser, 2004. "Social Comparisons in Ultimatum Bargaining," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 495-510, October.
    6. Maarten C.W. Janssen, 2006. "On the Strategic Use of Focal Points in Bargaining Situations," Tinbergen Institute Discussion Papers 06-040/1, Tinbergen Institute.
    7. Bolton Gary E. & Zwick Rami, 1995. "Anonymity versus Punishment in Ultimatum Bargaining," Games and Economic Behavior, Elsevier, vol. 10(1), pages 95-121, July.
    8. Rabin, Matthew, 1993. "Incorporating Fairness into Game Theory and Economics," American Economic Review, American Economic Association, vol. 83(5), pages 1281-1302, December.
    9. Janssen, Maarten C.W., 2006. "On the strategic use of focal points in bargaining situations," Journal of Economic Psychology, Elsevier, vol. 27(5), pages 622-634, October.
    10. Michał Ramsza, 2005. "Stability of pure strategy sampling equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 515-521, November.
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    Citations

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    Cited by:

    1. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    2. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2023. "Strategy sets closed under payoff sampling," Games and Economic Behavior, Elsevier, vol. 138(C), pages 126-142.
    3. Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2020. "Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis," MPRA Paper 99594, University Library of Munich, Germany.
    4. Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2021. "Instability of defection in the prisoner's dilemma under best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 197(C).
    5. Berkemer, Rainer & Starke, Jens & Kawamoto, Atsushi, 2023. "Sampling dynamics applied to the traveler's dilemma reveals non-Nash behavior," Games and Economic Behavior, Elsevier, vol. 142(C), pages 339-356.
    6. Sethi, Rajiv, 2021. "Stable sampling in repeated games," Journal of Economic Theory, Elsevier, vol. 197(C).
    7. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2022. "Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications," Journal of Economic Theory, Elsevier, vol. 206(C).
    8. Srinivas Arigapudi & Yuval Heller & Igal Milchtaich, 2020. "Instability of Defection in the Prisoner's Dilemma Under Best Experienced Payoff Dynamics," Papers 2005.05779, arXiv.org, revised Jan 2021.

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