Fairness in Multi-Proposer-Multi-Responder Ultimatum Game
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914900583907328 |
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| author | Krakovská, Hana Hanel, Rudolf Broom, Mark |
| author_facet | Krakovská, Hana Hanel, Rudolf Broom, Mark |
| contents | 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 behavior experimentally observed in the context of one vs. one Ultimatum Game scenarios. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fairness in Multi-Proposer-Multi-Responder Ultimatum Game Krakovská, Hana Hanel, Rudolf Broom, Mark Optimization and Control Computer Science and Game Theory Theoretical Economics 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 behavior experimentally observed in the context of one vs. one Ultimatum Game scenarios. 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. |
| title | Fairness in Multi-Proposer-Multi-Responder Ultimatum Game |
| topic | Optimization and Control Computer Science and Game Theory Theoretical Economics |
| url | https://arxiv.org/abs/2408.02410 |