Synthesizing safe coalition strategies

TL;DR

This paper investigates the challenge of synthesizing coalition strategies in concurrent games with an unknown number of agents to ensure safety, establishing the problem's computational complexity.

Contribution

It introduces the problem of coalition strategy synthesis for safety in games with arbitrary agent counts and proves its PSPACE-hardness and decidability in exponential space.

Findings

Existence of safe coalition strategies is PSPACE-hard.

Decidable in exponential space.

Applicable to arbitrary agent numbers.

Abstract

Concurrent games with a fixed number of agents have been thoroughly studied, with various solution concepts and objectives for the agents. In this paper, we consider concurrent games with an arbitrary number of agents, and study the problem of synthesizing a coalition strategy to achieve a global safety objective. The problem is non-trivial since the agents do not know a priori how many they are when they start the game. We prove that the existence of a safe arbitrary-large coalition strategy for safety objectives is a PSPACE-hard problem that can be decided in exponential space.