Cellular networks are often modeled using game theory, with base stations as players contending for a shared resource (the radio channel). Alternatively, if base stations are considered as nodes joined by edges (which represent significant interference), we obtain a graph structure. A game represented in this way is called a graphical game. We explore this representation by decomposing the network graph through tree decomposition and apply dynamic programming to find the optimum welfare, i.e., a resource allocation strategy profile most effective from the point of view of the overall network performance. We verify our approach through simulations and discuss the possibility of implementing this solution in a distributed manner.