Dicey Games: Shared Sources of Randomness in Distributed Systems

2026-01-26

AI Summary

This work addresses the challenge of maximizing team success probability in distributed multi-agent systems when agents can only coordinate through partially shared sources of randomness. To this end, the paper introduces “Dicey Games,” a formal framework that, for the first time, models and analyzes cooperative games under constrained shared randomness. Integrating tools from game theory, probabilistic modeling, and computational complexity, the study investigates the existence, representational form, and computational limits of optimal strategies. It demonstrates that even incomplete sharing of randomness can substantially enhance team performance. Notably, under certain sharing structures, achievable success probabilities exceed intuitive upper bounds, and optimal strategies can be efficiently synthesized via combinatorial optimization techniques.

Technology Category

• Multiagent Systems: Teamwork
• Game Theory and Economic Paradigms: Cooperative Game Theory
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• shared randomness
• distributed systems
• cooperative games
• randomness allocation
• Dicey Games

Innovation

• Dicey Games
• shared randomness
• distributed systems
• optimal strategy
• randomness allocation