City Research Online

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.

Publication Type:	Article
Additional Information:	Copyright: © 2025 Krakovská et al. This is an open access article distributed under the terms of the CreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology School of Science & Technology > Mathematics
SWORD Depositor:	Symplectic Administrator

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