Network Function Virtualization (NFV) simplifies the deployment of network services by leveraging virtualization technologies to make the management of network functions more flexible and cost efficient. The deployment of these services requires the allocation of Virtual Network Function-Forwarding Graph (VNF-FG), which implies placing and chaining VNFs according to the requests of VNF-FGs. In this paper, we consider the offline allocation of VNF-FG problem to improve resource utilization and reduce total costs. We focus on how VNF-FG demands are routed so as to optimize resource utilization without adding capacity to the infrastructure. Given a non-linear cost function associated to each network resource, we formulate the problem as a non-linear single-path routing problem in an extended graph. Then, we propose to adapt a single-path routing heuristic algorithm inspired from game theory to solve it. We show that this algorithm converges and establishes its approximation ratio in a number of cases. Experimental results obtained for different network topologies and different cost functions show that this algorithm provides very good quality solutions with a substantially lower computing times compared to the optimal solution.