The Pyro game: a slow intelligent fire

TL;DR

This paper introduces the Pyro game, a new two-player variant of the Firefighter problem, demonstrating that a single firefighter can contain the fire on certain grids and analyzing the game's complexity.

Contribution

The paper presents the Pyro game, a novel two-player model where the fire actively tries to maximize damage, and shows that one firefighter can contain the fire on the Cartesian grid.

Findings

A single firefighter can contain the fire on the Cartesian grid in the Pyro game.

The Pyro game differs from the Firefighter problem in that the fire actively seeks to maximize spread.

The paper analyzes the complexity of the Pyro game on infinite grids.

Abstract

In the Firefighter problem, a fire breaks out at a vertex of a graph and at each subsequent time step, the firefighter chooses a vertex to protect and then the fire spreads from each burned vertex to every unprotected neighbour. The problem can be thought of as a simplified model for the spread of gossip or disease in a network. We introduce a new two-player variation called the Pyro game, in which at each step, the fire spreads from one burned vertex to all unprotected neighbours of that vertex. The fire is no longer automated and aims to maximize the number of burned vertices. We show, that unlike the Firefighter problem, one firefighter can contain a fire on the Cartesian grid in the Pyro game. We also study both the Pyro Game and the Firefighter Problem on the infinite strong grid and the complexity of the Pyro game.