Use the following payoff matrix for a one-shot game to answer the accompanying q
ID: 1225946 • Letter: U
Question
Use the following payoff matrix for a one-shot game to answer the accompanying questions.
Which of these outcomes would you consider most likely?
b. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter?
(Click to select)AB
What outcome do you think would occur as a result?
c. Suppose player 2 can choose its strategy before player 1, that player 1 observes player 2’s choice before making her decision, and that this move structure is known by both players. What outcome would you expect?
PLEASE EXPLAIN
(-55,12) (12,-55) (25,25) (45,45) Player 2 Strategy 45, 45 12,-55 55, 12 25, 25 Player 1Explanation / Answer
Ans a. (45,45) and (25,25) are the 2 Nash equilibrium for the given game:
When Player 1 chooses strategy A, player 2 will maximize pay-off (monetary benefit) choosing strategy X and when Player 1 chooses strategy B, player 2 will maximize pay-off choosing strategy Y.
On the other hand, When Player 2 chooses strategy X, player 1 will maximize pay-off choosing strategy A and when Player 2 chooses strategy Y, player 1 will maximize pay-off choosing strategy B.
Simultaneous maximization of pay-offs ccur at the points (A,X) and (B,Y) giving respective pay-offs (45,45) and (25,25).
Most Likely Outcome:
We can infer the outcome (45,45) to be most likely since it gives more pay-off to both the players as compared to the other Nash Equilibrium (25,25).
Ans b. Player 1 is allowed to "communicate":
The maximumn pay-off that player 1 can get is 45 and that is using strategy A given of course that player 2 chooses X. It is not difficult to see that player 2 will choose X given player 1 has decided to choose A to maximize its own pay-off.
So, when player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions, it should utter strategy 'A'.
The resultant outcome would be (45,45).
Ans c. Player 2 is first mover:
The maximumn pay-off that player 2 can get is 45 and that is using strategy X given of course that player 1 chooses A. It is not difficult to see that player 1 will choose A given player 2 has decided to choose X to maximize its own pay-off.
So, the expected outcome in this case would be (45,45)