Cars cruising for parking adds a non negligible amount to traffic congestion and CO2 pollution. Hence, good parking management policies are required to reduce such discomfort. In this paper, we address this problem from two sides. First, we consider how local parking authorities called parking coordinators (PC) can optimize the distribution of the slots they manage through a full cooperation between them. Second, we model the problem as a congestion game, where vehicles act as players who will eventually choose the best parking garage for them, while minimizing the whole network cost. We study the effectiveness of both schemes (i.e, PC-aware and game theoretic approaches) in various contexts and compare them with the reference centralized model as well as a greedy approach. Simulation results show that our proposals provide high request satisfaction ratio, close to the optimal baseline approach and outperform the greedy method up to 30%, while ensuring a fair distribution of slots through the network.