Dicey Games: Shared Sources of Randomness in Distributed Systems
For researchers in distributed computing and game theory, this work formalizes the impact of shared randomness on team coordination, revealing non-intuitive advantages and computational challenges.
The paper introduces Dicey Games, a framework for analyzing distributed systems where players share limited sources of randomness. It shows that in a 4-player Matching Pennies variant, a team can win with probability greater than 1/4 by sharing randomness among pairs, and provides characterizations of optimal strategies and allocation of randomness sources.
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.