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Evolutionary models of the ultimatum game
Thesis (PhD)--Stellenbosch University, 2025.
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867613898621845504 |
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| access_status_str | Open Access |
| author | Van Schoor, Melt Philip |
| author2 | Burger, Rulof |
| author_browse | Burger, Rulof Van Schoor, Melt Philip |
| author_facet | Burger, Rulof Van Schoor, Melt Philip |
| author_sort | Van Schoor, Melt Philip |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description |
Thesis (PhD)--Stellenbosch University, 2025. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/132337 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:43:27.297Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/132337 Evolutionary models of the ultimatum game Van Schoor, Melt Philip Burger, Rulof Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Economics. Game theory Noncooperative games (Mathematics) Equilibrium (Economics) UCTD Thesis (PhD)--Stellenbosch University, 2025. van Schoor, M. 2025. Evolutionary Models of the Ultimatum Game. Unpublished doctoral dissertation. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/5e98f1d4-fab9-42b1-83a0-a0bee59af72b ENGLISH SUMMARY: This dissertation uses evolutionary models to improve our understanding of the structure of the ultimatum game and to provide and critically interpret explanations from evolutionary models for empirical results. Existing evolutionary models have established that stable evolutionary equilibria exist in which proposers make offers of relatively equal bargaining outcomes, while responders reject low but positive offers. These results are at odds with conventional game theoretic predictions, but consistent in some respects with observed human behaviour in experimental studies. The evolutionary dynamics leading to this result is not well understood for the full ultimatum game, as comprehensive analysis of dynamics have only been provided for a simplified minigame version of the game. Moreover, it has not been established that a minigame can constitute an adequate approximation for the full game. To address these deficiencies, conditional frequency dynamic analysis is used to formally link minigames to the full game, allowing the former to explain key results in the latter, particularly the existence and stability of non‑subgameperfect equilibria. The relevance of these results for experimental data is addressed next. Evolutionary models can be interpreted as frameworks for examining the cultural evolution of behavioural norms and preferences. This requires constructing microfoundations for the aggregate dynamics model that describes the stochastic process of individual‑level strategy revision. It is shown that certain assumptions made in the aggregate‑level model, which are necessary to predict relatively equal divisions, lead to unreasonable discrepancies in learning rates between individual agents in the proposer and responder populations. Furthermore, the results are not robust to stochastic disturbances infinite populations, limiting their applicability to empirical data and suggesting that additional model features are required to account for experimental findings of relatively equal divisions and rejections of low offers. The final research question investigated is whether allowing responders to build reputations can create the necessary incentives for higher offers and higher acceptance thresholds. However, a reputation for rejecting low offers can only be established if there is a sufficient frequency of low offers to reject, thus information must be treated as endogenous. A general endogenous information framework is developed to calculate endogenous information equilibria in two‑player population games, where the available information is consistent with the pattern of action profiles induced by it. The framework is used to explore different types of reputations, including negative reputations that harm responders when observed and positive reputations that benefit them when observed. It is shown that the different reputation mechanisms are complementary and can lead to relatively equal divisions and rejections of low offers, consistent with observed behaviour in experimental studies. These reputation‑based models also offer a plausible explanation for the evolution of relatively equal divisions in societies where such norms were initially absent – something that the baseline and earlier reputation‑based models fail to explain. AFRIKAANSE OPSOMMING: Geen opsomming beskikbaar. Doctoral 2025-06-04T08:14:51Z 2025-06-04T08:14:51Z 2025-03 Thesis https://scholar.sun.ac.za/handle/10019.1/132337 en_ZA Stellenbosch University x, 148 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Game theory Noncooperative games (Mathematics) Equilibrium (Economics) UCTD Van Schoor, Melt Philip Evolutionary models of the ultimatum game |
| title | Evolutionary models of the ultimatum game |
| title_full | Evolutionary models of the ultimatum game |
| title_fullStr | Evolutionary models of the ultimatum game |
| title_full_unstemmed | Evolutionary models of the ultimatum game |
| title_short | Evolutionary models of the ultimatum game |
| title_sort | evolutionary models of the ultimatum game |
| topic | Game theory Noncooperative games (Mathematics) Equilibrium (Economics) UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/132337 |
| work_keys_str_mv | AT vanschoormeltphilip evolutionarymodelsoftheultimatumgame |