Give some examples of games people play for entertainment that are strictly competitive ?
For a two-player game, two pure-strategy Nash equilibria (s1 , s2) and (t1 , t2) are called equivalent if ui(s) = ui(t) for i = 1, 2; they are called interchangeable if (s1 , t2) and (t1 , s2) also are Nash equilibria.
Mathematically prove that any two pure-strategy Nash equilibria of a two-player, strictly competitive game are both equivalent and interchangeable.