Problem_Set_3

# Problem_Set_3 - OR4350 Introduction to Game Theory Spring...

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OR4350 Introduction to Game Theory Spring 2010 Problem Set #3 Due : Wednesday, February 24, 2010 at noon in the dropbox (on 2 nd floor of Rhodes Hall) Reminder : Write your Section and NetID on the first page of your homework!!! Answers must always include complete explanations/justifications. 1. Binmore, Section 3.11, Number 6. Denote the two simple lotteries by L and M , respectively. The compound lottery in question is 1 3 L + 2 3 M . The expected values of L and M are: E L = \$3× 1 2 +(-\$2)× 1 2 = \$ 1 2 E M = (-\$2)× 1 2 +\$12× 1 6 +\$3× 1 3 = \$2 Hence the expected value of the compound lottery is: E ( 1 3 L + 2 3 M) = 1 3 × E L+ 2 3 × E M = 1 3 ×\$ 1 2 + 2 3 ×\$2 = \$ 3 2 2. Binmore, Section 3.11, Number 16. a. See Figure 1. b. At each node there is a positive probability that the game extends another round, which means there is no finite number for which you can guarantee the game ends in that number of moves or less. c. Suppose player I always chooses l . If the chance move selects L , the game ends in the outcome L ; if the chance move selects R , the game G is back to its origin. Thus the game continue forever if and only if the chance

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