Randomise Alone, Reach as a Team

2026-03-07

AI Summary

This work addresses the problem of coordinating multiple agents to reach a target state with high probability in distributed stochastic concurrent graph games, where no shared source of randomness is available and each agent’s private randomness is invisible to others. To formally model such settings, the paper introduces Individual-Randomized Alternating-Time Temporal Logic (IRATL) and proves that memoryless strategies suffice for solving threshold reachability objectives. Leveraging the existential theory of the reals (∃ℝ) and value iteration, the authors design an efficient solver and establish that threshold reachability is NP-hard while almost-sure reachability is NP-complete. This constitutes the first complete logical framework and complexity characterization for team-based stochastic games without shared randomness.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Game Theory and Economic Paradigms: Cooperative Game Theory

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

We study concurrent graph games where n players cooperate against an opponent to reach a set of target states. Unlike traditional settings, we study distributed randomisation: team players do not share a source of randomness, and their private random sources are hidden from the opponent and from each other. We show that memoryless strategies are sufficient for the threshold problem (deciding whether there is a strategy for the team that ensures winning with probability that exceeds a threshold), a result that not only places the problem in the Existential Theory of the Reals (\exists\mathbb{R}) but also enables the construction of value iteration algorithms. We additionally show that the threshold problem is NP-hard. For the almost-sure reachability problem, we prove NP-completeness. We introduce Individually Randomised Alternating-time Temporal Logic (IRATL). This logic extends the standard ATL framework to reason about probability thresholds, with semantics explicitly designed for coalitions that lack a shared source of randomness. On the practical side, we implement and evaluate a solver for the threshold and almost-sure problem based on the algorithms that we develop.

Problem

• concurrent graph games
• distributed randomisation
• team cooperation
• reachability
• randomness

Innovation

• distributed randomisation
• memoryless strategies
• Individually Randomised ATL
• threshold problem
• concurrent graph games