3 Cooperation problem and coordination problem Consider Table 1, a payoff matrix for Player A and Player B. a. Under what condition will Option 1 be a dominant strategy for Player A? b. Under what condition will Option 1 be a dominant strategy for Player B? c. Under what conditions will "both players choosing Option 1" be a Nash equilibrium? 2 Table 1 B chooses Option 1 B chooses Option 2 A chooses Option 1 (a, b) (c, d) A chooses Option 2 (e, f) (g, h) d. Under what conditions will "both players choosing Option 1" not be a Nash equilibrium? e. Under what conditions will "A choosing Option 2 while B choosing Option 1" be a Nash equilibrium? f. Now consider Table 2, another payoff matrix for Player A and Player B. Which situation will Player A like the best? Table 2 B chooses Option 1 B chooses Option 2 A chooses Option 1 (4, 3) (2, 1) A chooses Option 2 (1, 2) (100, 200) g. Which situation will Player B like the best? h. Is "both players choosing Option 2" a Nash equilibrium? Why? i. Is "both players choosing Option 1" a Nash equilibrium? Why? j. Which problem do we see now, a coordination problem or a cooperation problem? k. Now consider Table 3, another payoff matrix for Player A and Player B. Which problem do we see now, a coordination problem or a cooperation problem? Table 3 B chooses Option 1 B chooses Option 2 A chooses Option 1 (4, 3) (500, 1) A chooses Option 2 (1, 500) (400, 400)