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.
If player A chooses Bottom and player B chooses Right in a Nash equilibrium, then we know that

Question

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.  
If player A chooses Bottom and player B chooses Right in a Nash equilibrium, then we know that
A)b > 1 and d < 1. 
B)c < 1 and b < 1. 
C)b < 1 and c < d 
D) b < c and d < 1. 
E) a < 1 and b < d.

Quizplus · Accepted Answer

If player A chooses Bottom and player B chooses Right in a Nash equilibrium, it means that both players are making their best possible decisions given the other player's decision. 
For player A:
- If player B chooses Top, player A gets a payoff of b
- If player B chooses Bottom, player A gets a payoff of d
Since player A is choosing Bottom, they would prefer player B to choose Bottom so they can get a payoff of d, which is higher than the payoff of b. Therefore, player B choosing Bottom is the best choice for player A. 
For player B:
- If player A chooses Top, player B gets a payoff of c
- If player A chooses Bottom, player B gets a payoff of a
Since player B is choosing Right, they would prefer player A to choose Top so they can get a payoff of c, which is higher than the payoff of a. Therefore, player A choosing Top is the best choice for player B. 
So, b F1F1F1S1F1F1F10 1 and c F1F1F1S1F1F1F10d are both true, which means the answer is C.

In the Game Matrix Below, the First Payoff in Each