Strategies in Sabotage Games: Temporal and Epistemic Perspectives

2026-04-04

AI Summary

This study addresses strategic reasoning in sabotage games on dynamic graphs, where a runner and a demon interact under temporal evolution and asymmetric information. To this end, it introduces— for the first time in this domain—the alternating-time temporal logic ATL* and its epistemic extension, integrating them with dynamic graph models to construct a unified formal framework. This framework simultaneously captures the temporal behaviors of multiple agents and their epistemic uncertainties. By doing so, the approach substantially enhances the expressiveness and verifiability of strategies in graph-based games, offering a novel logical tool for multi-agent systems subject to temporal constraints and incomplete information.

Abstract

Sabotage games are played on a dynamic graph, in which one agent, called a runner, attempts to reach a goal state, while being obstructed by a demon who at each round removes an edge from the graph. Sabotage modal logic was proposed to carry out reasoning about such games. Since its conception, it has undergone a thorough analysis (in terms of complexity, completeness, and various extensions) and has been applied to a variety of domains, e.g., to formal learning. In this paper, we propose examining the game from a temporal perspective using alternating time temporal logic (ATL$^\ast$), and address the players' uncertainty in its epistemic extensions. This framework supports reasoning about winning strategies for those games, and opens ways to address temporal properties of dynamic graphs in general.

Problem

• sabotage games
• temporal logic
• epistemic reasoning
• dynamic graphs
• winning strategies

Innovation

• sabotage games
• alternating time temporal logic
• epistemic logic
• dynamic graphs
• winning strategies