A Multi-Step Model for Pie Cutting with Random Offers

Vladimir Mazalov () and Vladimir Yashin ()
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Vladimir Mazalov: Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk 185910, Russia
Vladimir Yashin: Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, Petrozavodsk 185910, Russia

Mathematics, 2024, vol. 12, issue 8, 1-10

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.

Keywords: fair pie cutting; arbitration procedure; consistent negotiations; punishment strategy; subgame perfect equilibrium; threshold strategies (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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