Abstract We consider the problem of computing a mixedstrategy Nash equilibrium (MSNE) in resource graph games (RGGs), a compact representation for games with an exponential number of strategies. At a high level, an RGG consists of a graphical representation of utility functions together with a representation of strategy spaces as convex polytopes. RGGs are general enough to capture a wide variety of games studied in literature, including congestion games and security games. In this paper, we provide the first Fully Polytnomial Time Approximation Scheme (FPTAS) for computing an MSNE in any symmetric multilinear RGG where its constraint moralized resource graph has bounded treewidth. Our FPTAS can be generalized to compute optimal MSNE, and to games with a constant number of player types. As a consequence, our FPTAS provides new approximation results for security games, network congestion games, and bilinear games.