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Punishing greediness in divide-the-dollar games

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  • Shiran Rachmilevitch

    (University of Haifa, Mount Carmel)

Abstract

Brams and Taylor 1994 presented a version of the divide-the-dollar game (DD), which they call DD1. DD1 suffers from the following drawback: when each player demands approximately the entire dollar, then if the least greedy player is unique, then this player obtains approximately the entire dollar even if he is only slightly less greedy than the other players. I introduce a parametrized family of 2-person DD games, whose “endpoints” (the games that correspond to the extreme points of the parameter space) are (1) a variant of DD1, and (2) a game that completely overcomes the greediness-related problem. I also study an n-person generalization of this family. Finally, I show that the modeling choice between discrete and continuous bids may have far-reaching implications in DD games.

Suggested Citation

  • Shiran Rachmilevitch, 2017. "Punishing greediness in divide-the-dollar games," Theory and Decision, Springer, vol. 82(3), pages 341-351, March.
    • Handle: RePEc:kap:theord:v:82:y:2017:i:3:d:10.1007_s11238-016-9568-6
    DOI: 10.1007/s11238-016-9568-6
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    1. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    2. de Clippel, Geoffroy & Moulin, Herve & Tideman, Nicolaus, 2008. "Impartial division of a dollar," Journal of Economic Theory, Elsevier, vol. 139(1), pages 176-191, March.
    3. Nejat Anbarci, 2001. "Divide-the-Dollar Game Revisited," Theory and Decision, Springer, vol. 50(4), pages 295-303, June.
    4. Esat Cetemen & Emin Karagözoğlu, 2014. "Implementing equal division with an ultimatum threat," Theory and Decision, Springer, vol. 77(2), pages 223-236, August.
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    Cited by:

    1. 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.
    2. 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.
    3. Atakan Dizarlar & Emin Karagözoğlu, 2023. "Kantian equilibria of a class of Nash bargaining games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(4), pages 867-891, August.
    4. Shiran Rachmilevitch, 2022. "Reasonable Nash demand games," Theory and Decision, Springer, vol. 93(2), pages 319-330, September.
    5. 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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