2. A game with two players, Player 1 and Player 2, is represented in the matrix below. Player 1 has two possible actions, U and D, and Player 2 has three possible actions, L, M and R. Remember that when the payoff from an outcome is written in the form x, y, it means that x is Player 1's payoff from that outcome, and y is Player 2's payoff from that outcome.
Player 2
L M R
Player U 10,3 4,2 1,7
1 D 7,5 6,7 5,4
(a) Write down Player 1's preferences over all of the outcomes of the game (that is, the order in which Player 1 likes the outcomes), noting any ties. Do the same for Player 2.
(b) Does player 1 have a dominant, or weakly dominant, action? Prove your answer.
(c) One of player 2's actions is strictly dominated. Identify which action it is, and find a strategy (possibly mixed) for player 2 that strictly dominates the action you identify.
