Extending Games beyond the Finite Horizon
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916999720861696 |
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| author | Sakahara, Kiri Sato, Takashi |
| author_facet | Sakahara, Kiri Sato, Takashi |
| contents | This paper argues that the finite horizon paradox, where game theory contradicts intuition, stems from the limitations of standard number systems in modelling the cognitive perception of infinity. To address this issue, we propose a new framework based on Alternative Set Theory (AST). This framework represents different cognitive perspectives on a long history of events using distinct topologies. These topologies define an indiscernibility equivalence that formally treats huge, indistinguishable quantities as equivalent. This offers criterion-dependent resolutions to long-standing paradoxes, such as Selten's chain store paradox and Rosenthal's centipede game. Our framework reveals new intuitive subgame perfect equilibria, the characteristics of which depend on the chosen temporal perspective and payoff evaluation. Ultimately, by grounding its mathematical foundation in different modes of human cognition, our work expands the explanatory power of game theory for long-horizon scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending Games beyond the Finite Horizon Sakahara, Kiri Sato, Takashi Computer Science and Game Theory 91A44, 91A20, 28E05 This paper argues that the finite horizon paradox, where game theory contradicts intuition, stems from the limitations of standard number systems in modelling the cognitive perception of infinity. To address this issue, we propose a new framework based on Alternative Set Theory (AST). This framework represents different cognitive perspectives on a long history of events using distinct topologies. These topologies define an indiscernibility equivalence that formally treats huge, indistinguishable quantities as equivalent. This offers criterion-dependent resolutions to long-standing paradoxes, such as Selten's chain store paradox and Rosenthal's centipede game. Our framework reveals new intuitive subgame perfect equilibria, the characteristics of which depend on the chosen temporal perspective and payoff evaluation. Ultimately, by grounding its mathematical foundation in different modes of human cognition, our work expands the explanatory power of game theory for long-horizon scenarios. |
| title | Extending Games beyond the Finite Horizon |
| topic | Computer Science and Game Theory 91A44, 91A20, 28E05 |
| url | https://arxiv.org/abs/2510.08453 |