Unattainability of Common Knowledge in Asymmetric Games with Imperfect Information
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915094508601344 |
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| author | Farestam, Fabian Gurov, Dilian |
| author_facet | Farestam, Fabian Gurov, Dilian |
| contents | In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has no information of the state of the game, whereas the other agent has perfect information of the state but cannot act or observe the other agent's actions. This duality manifests an extreme form of asymmetry, and how differing abilities influence the possibility of attaining common knowledge. Using Kripke structures and epistemic logic we demonstrate that, under these conditions, common knowledge of the current game state becomes unattainable. Our findings advance the discussion on the strategic limitations of knowledge in environments where information and action are unevenly distributed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04199 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unattainability of Common Knowledge in Asymmetric Games with Imperfect Information Farestam, Fabian Gurov, Dilian Multiagent Systems Computer Science and Game Theory Logic in Computer Science 03B42 (Primary) 91A05 91A27, 91A43 (Secondary) I.2.4; I.2.11; F.4.1; G.2.2 In this paper, we present a conceptual model game to examine the dynamics of asymmetric interactions in games with imperfect information. The game involves two agents with starkly contrasting capabilities: one agent can take actions but has no information of the state of the game, whereas the other agent has perfect information of the state but cannot act or observe the other agent's actions. This duality manifests an extreme form of asymmetry, and how differing abilities influence the possibility of attaining common knowledge. Using Kripke structures and epistemic logic we demonstrate that, under these conditions, common knowledge of the current game state becomes unattainable. Our findings advance the discussion on the strategic limitations of knowledge in environments where information and action are unevenly distributed. |
| title | Unattainability of Common Knowledge in Asymmetric Games with Imperfect Information |
| topic | Multiagent Systems Computer Science and Game Theory Logic in Computer Science 03B42 (Primary) 91A05 91A27, 91A43 (Secondary) I.2.4; I.2.11; F.4.1; G.2.2 |
| url | https://arxiv.org/abs/2501.04199 |