In this work, we consider a game theory approach to deal with an inverse problem related to the Stokes system. The problem consists in detecting the unknown point-forces acting on the fluid from incomplete measurements on the boundary of a domain. The approach that we propose deals simultaneously with the reconstruction of the missing data and the determination of the unknown point-forces. The solution is interpreted in terms of Nash equilibrium between both problems. We develop a new point-force detection algorithm, and we present numerical results to illustrate the efficiency and robustness of the method.