We present a particular disaster response project scheduling problem (DRPSP) motivated by Fukushima's nuclear accident of Japan in 2011. We describe the problem as $MPS;R,N \vert prec, d_n \vert \sum c_k f(r_k (S))$ by using Hartmann and Briskorn scheme and formulate a mixed integer linear programming (MILP) model. Due to the NP-hardness of the problem, we propose a resolution method based on game theory. This method associates the DRPSP to a non-cooperative game model, such that game solution is a feasible solution of the problem. In order to explore the potential of the proposed model and the performance of the resolution method, computational experiments are carried out. The results of resolution method show on average, that the method finds a feasible solution with a difference of 15.44% with respect to optimal solution within one percent of the time required by the MILP over GAMS 22.7.2/CPLEX 11.0.