In this thesis, we consider exploring a 2-D environment with multiple robots by modelling the problem as a Potential Game rather than using conventional frontier-based dynamic programming algorithms. A potential game is a type of game that results in coordinated behaviours amongst players. This is done by enforcing strict rules for each player in selecting an action from its action set. As part of this game, we define a potential function for the game that is meaningful in terms of achieving the greater objective of exploring a space. Furthermore, an objective function is assigned for each player from this potential function. We then create algorithms for the exploration of obstacle-filled bounded spaces, and demonstrate through simulation how it outperforms uncoordinated algorithms by reducing the time needed to uncover the space.