Paper: Dicey Games: Shared Sources of Randomness in Distributed Systems (at LICS 2026)

Authors: Léonard Brice Thomas A. Henzinger K. S. Thejaswini

Open access: https://doi.org/10.4230/LIPIcs.LICS.2026.23

Abstract

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.

BibTeX

  @InProceedings{BriceHenzingerTheja-DiceyGamesSharedSou,
    author = 	 {Léonard Brice and Thomas A. Henzinger and K. S. Thejaswini},
    title = 	 {Dicey Games: Shared Sources of Randomness in Distributed Systems},
    booktitle =  {Proceedings of the Forty-First Annual Symposium on Logic in Computer Science (LICS 2026)},
    year =	 {2026},
    month =	 {July}, 
    pages =      {23:1--23:26},
    location =   {Lisbon, Portugal}, 
    publisher =	 {Schloss Dagstuhl -- Leibniz-Zentrum für Informatik},
    doi =        {10.4230/LIPIcs.LICS.2026.23}
  }