This study investigates the potential of non-additive path-based pricing for congestion management in urban transportation networks. We propose a novel path-based reward credit scheme to provide commuter incentives with the goal of reducing traffic congestion. We consider that a known proportion of commuters subscribe to this reward credit scheme and may earn credits when traveling in the network. We introduce a bilevel optimization formulation to determine optimal non-additive, path-based reward credits under traffic equilibrium conditions. In this formulation, the follower problem is a parameterized user equilibrium traffic assignment problem with two classes of users and non-additive path costs. We develop a single-level reformulation based on its first-order optimality conditions and derive theoretical properties of the reward credit scheme. Customized branch-and-bound algorithms are designed to solve the problem. We also introduce a heuristic approach that repeatedly solves parameterized follower problems to enhance scalability. We report numerical results that demonstrate the computational efficiency of the proposed methods over a benchmarking approach. We conduct a comprehensive evaluation of this path-based reward credit scheme compared with a link-based subsidy pricing scheme. We find that, on average, under a limited budget and a user participation level of at least 40%, the proposed path-based incentive mechanism yields larger reductions in traffic congestion over link-based approaches.