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hw1 - S'11 Prof Stahl 354K Game Theory Problem Set No 1 Due...

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S'11 Prof. Stahl 354K Game Theory Problem Set No. 1 Due: Tuesday, Jan 25 1) Consider the uncertainty associated with drawing a card from a deck of cards. List the sample and event spaces (you do not have to list all possibilities but list the categories). How would you assign a probability function to this uncertainty? (Dutta, chapter 26: 14) 2) Consider a uniform distribution between the two values 0 and 1. What is the probability that x lies between 0 and 1/3? What then is the probability that x lies between 1/3 and 1? What is the probability that x lies between any two fractions, a and b ? (Dutta, chapter 26: 15) 3) Consider the following game. Let us write its table with probabilities instead of payoffs; that is, the probability in the cell (U,C) represents the probability that player 1 will play U and player 2 will play C. (Dutta, chapter 26: 22) 1\2 L C R U 0 1/12 2/7 M 1/12 1/6 0 D 1/6 0 3/14 Find the conditional probability of L given U. Repeat with the conditional probability of C given U.
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