  In this paper we formulate the homogeneous two- and three-dimensional
self-reconfiguration problem over discrete grids as a constrained potential
game. We develop a game-theoretic learning algorithm based on the
Metropolis-Hastings algorithm that solves the self-reconfiguration problem in a
globally optimal fashion. Both a centralized and a fully distributed algorithm
are presented and we show that the only stochastically stable state is the
potential function maximizer, i.e. the desired target configuration. These
algorithms compute transition probabilities in such a way that even though each
agent acts in a self-interested way, the overall collective goal of
self-reconfiguration is achieved. Simulation results confirm the feasibility of
our approach and show convergence to desired target configurations.
