Definition 2 An action profile a∗ = {a∗i}i∈N is a strictly dominant strategy equilibrium if a∗i is a strictly dominant action for each player i ∈ N.
(a) Write down a 2 player game that does not possess a strictly dominant strategy equilibrium.
(b) Prove that a strictly dominant strategy equilibrium of Γ is a Nash equilibrium of Γ.
(c) Prove that there can exist at most one strictly dominant strategy equilibrium in any normal-form game Γ.