A two-player game is symmetric if the two players have the same strategy set S1 = S2 and the payoff functions satisfy u1(s1, s2) = u2(s2, s1) for each s1, s2 ∈ S1.
Prove that the set of equilibria of a two-player symmetric game is a symmetric set: if (s1, s2) is an equilibrium, then (s2, s1) is also an equilibrium.