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Fairness in the multi-proposer-multi-responder ultimatum game

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  • Hana Krakovská
  • Rudolf Hanel
  • Mark Broom

Abstract

The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the Ultimatum Game, called the Multi-Proposer-Multi-Responder Ultimatum Game. In this model, multiple responders and proposers simultaneously interact in a one-shot game, introducing competition both within proposers and within responders. We derive subgame-perfect Nash equilibria for all scenarios and explore how these non-trivial values might provide insight into proposal and rejection behaviour experimentally observed in the context of one vs. one Ultimatum Game. Additionally, by considering the asymptotic numbers of players, we propose two potential estimates for a “fair” threshold: either 31.8% or 36.8% of the pie (share) for the responder.

Suggested Citation

  • Hana Krakovská & Rudolf Hanel & Mark Broom, 2025. "Fairness in the multi-proposer-multi-responder ultimatum game," PLOS ONE, Public Library of Science, vol. 20(3), pages 1-20, March.
    • Handle: RePEc:plo:pone00:0319178
    DOI: 10.1371/journal.pone.0319178
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