(In this and all other questions in which a game matrix is given, Player 1 chooses the row, Player 2 chooses the column, and if there is a Player 3, she chooses the matrix.)  A Bc 2,1 -2,-1d -1,-1 1,3In the 2 player game above, what is Player 1's expected payoff given the mixed strategy profile ((1/4, 3/4), (2/3, 1/3))? Round your answer to two decimal places (e.g. 2.15).

Consider the below payoff matrix. Player 1 chooses rows and Player 2 chooses columns.  A BX 15 , 0 0 , 8Y 0 , 39 15 , 0Denote the probability of “X" for Player 1 as p, and the probability of “A” for Player 2 as q. What is the value of q in the mixed-strategy Nash equilibrium of this game? Round your answer to two decimal places (e.g. 0.15).

In the game matrix below, the first payoff in each pair goes to player A who chooses the row, and the second payoff goes to player B, who chooses the column. Let a, b, c, and d be positive constants. Left；Top a,1 ，Bottom 1.c Right：Top b.l，Bottom 1,d If player A chooses Bottom and player B chooses Right in a Nash equilibrium, then we know that

In this and all other questions in which a game matrix is given, Player 1 chooses the row, Player 2 chooses the column, and if there is a Player 3, she chooses the matrix.)   A  B  C  D a  1,2  1,0  2,1  0,-3 b  1,4  3,5  2,0  1,2 c  -1,1  4,1  4,-1  -1,2 d  0,0  -2,-1  5,2  -1,0Select all of the following that are Nash equilibria in the above game. (Note: partial credit is possible for this question.) (1,2) (a,A) (d,C) (b,B) (3,5) (c,B)

Consider the three player normal form game described by the payoff matrices below.  Players 1 and 2 have two choices each while player 3 has three choices.  Player 3 choices correspond to each of the three matrices.  The payoffs in each cell are the payoffs of player 1, player 2, and player 3 respectively.Player 3 chooses U:  L Rl 1,0,1 0,1,1r 0,1,1 1,0,0Player 3 chooses M:  L Rl 1,1,1 -1,-1,1r -1,-1,1 1,1,1Player 3 chooses D:  L Rl 0,1,0 1,0,1r 1,0,1 0,1,1Which of the following statements is true? M is a strongly dominant action for player 3. U is a weakly dominant action for player 3. M is a weakly dominant action for player 3. D is a weakly dominant action for player 3.

In a 3-player game, S subscript 1 equals S subscript 2 equals S subscript 3 equals left square bracket 0 comma 5 right square bracket. Each player obtains a payoff of 1 if her strategy equals the absolute value of the difference of the strategies of the other two players, and a payoff of 0 otherwise. Choose all of the following strategy profiles which are Nash equilibria. (0,0,0) (4,4,4) (2,2,4) (2,1,3) (2,2,0) (0,2,4)