  We consider the problem of computing Nash equilibria in potential games where
each player's strategy set is subject to private uncoupled constraints. This
scenario is frequently encountered in real-world applications like road network
congestion games where individual drivers adhere to personal budget and fuel
limitations. Despite the plethora of algorithms that efficiently compute Nash
equilibria (NE) in potential games, the domain of constrained potential games
remains largely unexplored. We introduce an algorithm that leverages the
Lagrangian formulation of NE. The algorithm is implemented independently by
each player and runs in polynomial time with respect to the approximation
error, the sum of the size of the action-spaces, and the game's inherent
parameters.
