In this paper a proof for First Order Stochastic Dominance for capacity constrained oligopolies exhibiting equilibrium in mixed strategies is derived. The result is an extension of Levitan and Shubik (1972) where they derive the mixed strategy equilibrium for quantity constrained oligopolies. I show that their result has applications in policy issues in Regulation and Trade Theory. The proof of First Order Stochastic Dominance facilitates the comparison of expected prices across different experimental/trade policy designs, enlarging the qualitative implications of the results derived by Levitan et al.