Nash equilibrium
proof: Price of stability is equal to best Nash equilibrium divided by OPTimum. Therefore, in order to prove that Price of stability = 1 it is sufficient to prove that the optimum is equal to the best Nash equilibrium. In order to prove that, it is sufficient to prove that there is an OPTimum solution which is in Nash equilibrium, since if the OPTimum is also Nash equilibrium it is especially best Nash equilibrium.