In this paper, we propose a game-theoretic solution to the parking problem, by exploiting a strategic-reasoning approach for multi-agent systems. Precisely, cars are modeled by agents interacting among them in a multi-player game setting, whose aim is to get a free slot parking-place satisfying their own constraints. The overall assignment is then given as a Nash equilibrium solution. We come up with an algorithm (and its implementation in a tool) that works in quadratic time. We give evidence of the benefits of our approach by running our tool on a large hospital parking space.