Dicey Games: Shared Sources of Randomness in Distributed Systems

TL;DR

Dicey Games introduces a formal framework to analyze how shared randomness sources among players in distributed systems influence strategic outcomes, with implications for optimal strategy design and resource allocation.

Contribution

The paper characterizes the existence, representation, and computational complexity of optimal strategies in Dicey Games, a new model inspired by distributed systems with shared randomness.

Findings

Sharing a common randomness source significantly increases winning probability.

Sharing pairwise randomness can outperform sharing a single common source.

The framework enables analysis of optimal strategies and resource allocation in distributed settings.

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.