(Table: Jim, Dan Payoff Table) Refer to the table. Which of the following outcomes is NOT a Nash equilibrium? I. (12, 12) II. (4, 4) III. (8, 8) IV. (3, 3)

Question

(Table: Jim, Dan Payoff Table) Refer to the table. Which of the following outcomes is NOT a Nash equilibrium?  I. (12, 12) II. (4, 4) III. (8, 8) IV. (3, 3)

Quizplus · Accepted Answer

To determine the Nash equilibria, we look for each player's dominant strategy. From the table, it can be seen that for Jim, his dominant strategy is to choose 4 regardless of Dan's choice, and for Dan, his dominant strategy is to choose 4 regardless of Jim's choice. Therefore, the only Nash equilibrium is at (4, 4). 
Option I: (12, 12) is not a Nash equilibrium since Jim would prefer to switch to 8, resulting in a payoff of (8, 4) rather than (12, 0). 
Option II: (4, 4) is a Nash equilibrium as both Jim and Dan are already playing their dominant strategy. 
Option III: (8, 8) is not a Nash equilibrium since Jim would prefer to switch to 12, resulting in a payoff of (12, 0) rather than (8, 8). 
Option IV: (3, 3) is not a Nash equilibrium since Dan would prefer to switch to 4, resulting in a payoff of (4, 2) rather than (3, 3).

(Table: Jim, Dan Payoff Table) Refer to the Table