Question

(a) (5 points) Do the players have any strategies which are dominated? Any dominant strategies?

3. In a 2-player simultaneous game, Players 1 and 2 have three strategies: A, B, and C. Both players have the same payoffs, which are depicted in Figure 1 (so 4 means (4,4)). P2 A B C P1 B 0.5 0.5 0.5 Figure 1: Stock Market Game

(b) (2 points) Suppose you could create a new strategy (D) which consisted of A x = 75% of the time and C 1 − x = 25% of the time. If your payoff from this new strategy is the average of your payoffs from A and C (given the percentages), what is the payoff of D? Add it to the matrix.

(c) (3 points) Repeat part (a); is there a difference? Why or why not?

(d) (5 points) D is an example of a mixed strategy since it’s a mixture of other strategies. How would you modify the process of IESDS to include mixed strategies if x can vary? Explain.

Answer 1

Ans a) Yes both of them have a dominant startegy to use Strategy A as the payoff for both of them is maximum there that is 4. This way they both get the maximum benefit and least risk

Ans b) In this case they would go with either (A,A) or (A,B) as this is where they get the maximum payoff when talking about 75% time. Next 25% of the time the will be using Strategy C where player 1 will choose strategy C to maximize and player 2 will do the same because we assume that both players are rational.

so the matrix to be added will be

3, 3.25 , 1

Ans c) They still have the same dominant strategy as it has better payoff and lower risk