(Increasing payoffs and eliminating actions in strictly competitive games) Let G be a strictly competitive game that has a Nash equilibrium.
a. Show that if some of player 1's payoffs in G are increased in such a way that the resulting game Gt is strictly competitive then Gt has no equilibrium in which player 1 is worse off than she was in an equilibrium of G. (Note that Gt may have no equilibrium at all.)
b. Show that the game that results if player 1 is prohibited from using one of her actions in G does not have an equilibrium in which player 1's payoff is higher than it is in an equilibrium of G.
c. Give examples to show that neither of the above properties necessarily holds for a game that is not strictly competitive.