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?
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?