Enforcing local volume constraints in the design problem turns out to be an efficient approach to increase structural robustness against uncertainties (Wu et al., 2017). By constraining locally the available amount of material, the optimized design exhibits infill patterns which reflects a more uniform and periodic distribution of the material. This method can notably produce results exhibiting bone-like structures which are known to be robust against load uncertainty. Compared to a deterministic approach, the robustness is often achieved at the cost of reducing the component stiffness (Tromme et al., 2017). However, the justification of using local volume constraints has not been well discussed in the context of robust topology optimization. Moreover, no standard methodology exists to determine the local volume constraint upper bound. This study aims to explain the relationship between robustness and local volume constraints and to propose a method defining the upper bound of local volume constraints for a given failure distribution. To compute the failure probability distribution, a game theory approach is adopted. A standard design problem is solved to illustrate the developed method.