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Implementing equal division with an ultimatum threat

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  • Esat Cetemen
  • Emin Karagözoğlu

Abstract

We modify the payment rule of the standard divide the dollar (DD) game by introducing a second stage and thereby resolve the multiplicity problem and implement equal division of the dollar in equilibrium. In the standard DD game, if the sum of players’ demands is less than or equal to a dollar, each player receives what he demanded; if the sum of demands is greater than a dollar, all players receive zero. We modify this second part, which involves a harsh punishment. In the modified game $$(D\!D^{\prime })$$ ( D D ′ ) , if the demands are incompatible, then players have one more chance. In particular, they play an ultimatum game to avoid the excess. In the two-player version of this game, there is a unique subgame perfect Nash equilibrium in which players demand (and receive) an equal share of the dollar. We also provide an $$n$$ n -player extension of our mechanism. Finally, the mechanism we propose eliminates not only all pure strategy equilibria involving unequal divisions of the dollar, but also all equilibria where players mix over different demands in the first stage. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Esat Cetemen & Emin Karagözoğlu, 2014. "Implementing equal division with an ultimatum threat," Theory and Decision, Springer, vol. 77(2), pages 223-236, August.
    • Handle: RePEc:kap:theord:v:77:y:2014:i:2:p:223-236
    DOI: 10.1007/s11238-013-9394-z
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    Cited by:

    1. Shiran Rachmilevitch, 2017. "Punishing greediness in divide-the-dollar games," Theory and Decision, Springer, vol. 82(3), pages 341-351, March.
    2. Emin Karagözoğlu & Shiran Rachmilevitch, 2018. "Implementing egalitarianism in a class of Nash demand games," Theory and Decision, Springer, vol. 85(3), pages 495-508, October.
    3. Emin Karagözoğlu & Kerim Keskin & Çağrı Sağlam, 2023. "(In)efficiency and equitability of equilibrium outcomes in a family of bargaining games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 175-193, March.
    4. Emin Karagözoğlu & Martin G. Kocher, 2019. "Bargaining under time pressure from deadlines," Experimental Economics, Springer;Economic Science Association, vol. 22(2), pages 419-440, June.
    5. Shiran Rachmilevitch, 2022. "Reasonable Nash demand games," Theory and Decision, Springer, vol. 93(2), pages 319-330, September.
    6. Gonzalez-Sanchez, Eric & Loyola, Gino, 2024. "Ultimatum bargaining with envy under incomplete information," Mathematical Social Sciences, Elsevier, vol. 127(C), pages 1-11.
    7. Shiran Rachmilevitch, 2020. "Rewarding moderate behavior in a dynamic Nash Demand Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 639-650, June.

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