For each statement give 2x2 matrix that shows it is false. (I'd start by looking at the games I put up in class, Prisoner's Dilemma, Battle of the Sexes, World's Dumbest Game, etc.) When I talk about Pareto efficiency or domination assume it's strong.
(a) If an outcome is a Nash equilibrium outcome, one player or the other gets the highest payoff the player can get in the matrix.
(b) For each outcome consider the sum of the two payoffs. A Nash equilibrium always gives the two players their highest sum.
(c) A Pareto-efficient outcome will be a Nash equilibrium.
(d) A Nash equilibrium outcome will be Pareto-efficient.
(e) There can never be two Nash equilibria in the same Row.
(f) There is no 2x2 game where all four outcomes are Nash equilibrium outcomes.
(g) If an outcome is Pareto-efficient it cannot be in a dominated row or in a dominated column. (h) There is no 2x2 game where all four outcomes are Pareto-efficient.
(i) There is no 2x2 game where one player has a dominating strategy and the other player does not.