# Reachability Games in Dynamic Epistemic Logic

## TL;DR

This paper introduces reachability games within Dynamic Epistemic Logic, analyzing strategies for controllers and agents with perfect and imperfect information, and provides decidability results for various action types.

## Contribution

It formalizes reachability games in DEL, extending epistemic planning to multi-agent settings with new decidability and undecidability results.

## Key findings

- Decidability results for controller strategies with public actions
- Undecidability results for distributed strategies among agents
- Extension of epistemic planning to multi-agent, imperfect information scenarios

## Abstract

We define reachability games based on Dynamic Epistemic Logic (DEL), where the players' actions are finely described as DEL action models. We first consider the setting where an external controller with perfect information interacts with an environment and aims at reaching some epistemic goal state regarding the passive agents of the system. We study the problem of strategy existence for the controller, which generalises the classic epistemic planning problem, and we solve it for several types of actions such as public announcements and public actions. We then consider a yet richer setting where agents themselves are players, whose strategies must be based on their observations. We establish several (un)decidability results for the problem of existence of a distributed strategy, depending on the type of actions the players can use, and relate them to results from the literature on multiplayer games with imperfect information.