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 following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L ,Sally gets a payoff of 3 and John has a payoff of 7. If Sally plays T and John R, Sally’s payoff is 2 and John gets 1. If Sally Chooses B and John L, the payoffs are 1 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 4 to Sally and 3 to John. What are the Nash equilibria of the game?Group of answer choices(T,R)(B,R)(T,L) and (B,R)(T,L)None of the above

Consider the following game represented in normal form. Terry and Kerry are roommates who must make decisions about cleaning. Terry’s payoff is the first number in each cell and a higher number is a better outcome. Assume that Terry makes his decision first, if so what is the Nash Equilibrium of this game:   Kerry  CleanDon’t cleanTerryClean( 8, 2 )( 3, 5 )Don’t clean( 10, 3 )( 4, 1 )Group of answer choicesTerry will clean and Kerry will not clean.Terry will not clean and Kerry will not clean.Terry will not clean and Kerry will clean.Terry will clean and Kerry will clean.More information is required to answer this question.

In a Nash equilibrium

Consider the following game. Player A and B simultaneously choose to work on either Project 1 (P1) or Project 2 (P2). The payoffs are as follows: if both players choose P1 the payoffs are 6 to A and 2 to B; if A chooses P1 and B chooses P2 the payoffs are 0 to each party; likewise, if A chooses P2 and B chooses P1 the payoffs are 0 to each party; and, finally, if A chooses P2 and B P2 the payoffs are 3 to both players. What are all of the Nash equilibria of this game? a. (P1, P1) b. (P1, P1), (P2, P2) c. (P1, P1), (P2, P2) and (Player A plays P1 with probability 1/3, Player B plays P1 with probability 1/2) d. (P1, P1), (P2, P2) and (Player A plays P1 with probability 3/5, Player B plays P1 with probability 1/3) e. (P1, P2), (P2, P2) and (Player A plays P1 with probability 1/2, Player B plays P1 with probability 2/3)