Dicey Games: Shared Sources of Randomness in Distributed Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910215125860352 |
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| author | Brice, Léonard Henzinger, Thomas A. Thejaswini, K. S. |
| author_facet | Brice, Léonard Henzinger, Thomas A. Thejaswini, K. S. |
| contents | Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team players randomise independently, they win with probability 1/8; if all players share a common source of randomness, they win with probability 1/2. What happens when each pair of team players shares a source of randomness? Can the team do better than win with probability 1/4? The surprising (and nontrivial) answer is yes! We introduce Dicey Games, a formal framework motivated by the study of distributed systems with shared sources of randomness (of which the above example is a specific instance). We characterise the existence, representation and computational complexity of optimal strategies in Dicey Games, and we study the problem of allocating limited sources of randomness optimally within a team. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18303 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dicey Games: Shared Sources of Randomness in Distributed Systems Brice, Léonard Henzinger, Thomas A. Thejaswini, K. S. Computer Science and Game Theory Logic in Computer Science Multiagent Systems Consider a 4-player version of Matching Pennies where a team of three players competes against the Devil. Each player simultaneously says "Heads" or "Tails". The team wins if all four choices match; otherwise the Devil wins. If all team players randomise independently, they win with probability 1/8; if all players share a common source of randomness, they win with probability 1/2. What happens when each pair of team players shares a source of randomness? Can the team do better than win with probability 1/4? The surprising (and nontrivial) answer is yes! We introduce Dicey Games, a formal framework motivated by the study of distributed systems with shared sources of randomness (of which the above example is a specific instance). We characterise the existence, representation and computational complexity of optimal strategies in Dicey Games, and we study the problem of allocating limited sources of randomness optimally within a team. |
| title | Dicey Games: Shared Sources of Randomness in Distributed Systems |
| topic | Computer Science and Game Theory Logic in Computer Science Multiagent Systems |
| url | https://arxiv.org/abs/2601.18303 |