Due to restricted budgets of relief organizations, costs of hiring transportation service providers steer distribution decisions and limit the impact of disaster relief. To improve the success of future humanitarian operations, it is of paramount importance to understand this relationship in detail and to identify mitigation actions, always considering the interdependencies between multiple independent actors in humanitarian logistics. In this paper, we develop a game-theoretic model in order to investigate the influence of transportation costs on distribution decisions in long-term relief operations and to evaluate measures for improving the fulfillment of beneficiary needs. The equilibrium of the model is a Generalized Nash Equilibrium, which has had few applications in the supply chain context to date. We formulate it, utilizing the construct of a Variational Equilibrium, as a Variational Inequality and perform numerical simulations in order to study the effects of three interventions: an increase in carrier competition, a reduction of transportation costs and an extension of framework agreements. The results yield important implications for policy makers and humanitarian organizations (HOs). Increasing the number of preselected carriers strengthens the bargaining power of HOs and improves impact up to a certain limit. The limit is reached when carriers set framework rates equal to transportation unit costs. Reductions of transportation costs have a consistently positive, but decreasing marginal benefit without any upper bound. They provide the highest benefit when the bargaining power of HOs is weak. On the contrary, extending framework agreements enables most improvements when the bargaining power of HOs is strong.