Collaborative Predatory-Prey Hex World

Problem

The collaborative predator-prey hex world is an variant of the predator-prey hex world in which a team of predators chase a single moving prey. The predators must work together to capture a prey. The prey moves randomly to a neighboring cell that is not occupied by a predator.

Observations and Rewards

Predators also only make noisy local observations of the environment. Each predator $i$ detects whether a prey is within a neighboring cell $\mathcal{O}^i = \{\text{prey}, \text{nothing}\}$. The predators are penalized with a $−1$ reward for movement. They receive a reward of $10$ if one or more of them capture the prey, meaning they are in the same cell as the prey. At this point, the prey is randomly assigned a new cell, signifying the arrival of a new prey for the predators to begin hunting.