Two people agree to play the following game: The first writes either a 1 or 4 on

Question

Two people agree to play the following game: The first writes either a 1 or 4 on a slip of paper, and at the same time the second writes either 0 or 3 on another slip of paper. If the sum of the two numbers is odd, the first person wins this amount in dollars (i.e. if the sum is 7, the first person wins $7); otherwise, the second person wins $2.

a. Construct the payoff matrix using positive values for the first person’s gain, and negatives for losses.

b. Determine the probabilities of the strategies for the first player.

c. Determine the expected gain/loss for the first player.

Explanation / Answer

Part (a) Pay-off for Person 1

Person 1

Person 2

0

3

1

1

- 4

4

- 5

7

Part (b)

Assuming equal probability for the two numbers, probabilities of the strategies for the first player are

Person 1

Person 2

0

3

1

1/4

1/ 4

4

1/4

1/4

Part (c)

Expected gain/loss for the first player

= {1 x (1/4)} +{- 4 x (1/4)} + {- 5 x (1/4)} + {7 x (1/4)} = - ¼ (loss) ANSWER

Person 1

Person 2

0

3

1

1

- 4

4

- 5

7

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.