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A Multi-Step Model for Pie Cutting with Random Offers

Author

Listed:
  • Vladimir Mazalov

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk 185910, Russia
    Department of Applied Mathematics and Informatics, Yaroslav-the-Wise Novgorod State University, Novgorod 173003, Russia)

  • Vladimir Yashin

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk 185910, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, Petrozavodsk 185910, Russia)

Abstract

The problem of dividing a pie between two persons is considered. An arbitration procedure for dividing the pie is proposed, in which the arbitrator is a random number generator. In this procedure, the arbitrator makes an offer to the players at each step, and the players can either accept or reject the arbitrator’s offer. If there is no consensus, negotiations move on to the next step. At the same time, the arbitrator punishes the rejecting player by reducing the amount of the resource in favor of the consenting player. A subgame perfect equilibrium is found in the process.

Suggested Citation

  • Vladimir Mazalov & Vladimir Yashin, 2024. "A Multi-Step Model for Pie Cutting with Random Offers," Mathematics, MDPI, vol. 12(8), pages 1-10, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1150-:d:1373903
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    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    3. Predtetchinski, Arkadi, 2011. "One-dimensional bargaining," Games and Economic Behavior, Elsevier, vol. 72(2), pages 526-543, June.
    4. Cho, Seok-ju & Duggan, John, 2003. "Uniqueness of stationary equilibria in a one-dimensional model of bargaining," Journal of Economic Theory, Elsevier, vol. 113(1), pages 118-130, November.
    5. Cardona, Daniel & Ponsati, Clara, 2007. "Bargaining one-dimensional social choices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 627-651, November.
    6. Eraslan, Hulya, 2002. "Uniqueness of Stationary Equilibrium Payoffs in the Baron-Ferejohn Model," Journal of Economic Theory, Elsevier, vol. 103(1), pages 11-30, March.
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