# hw4 - (p 0 0 1-p and \$50 for sure(c For what value of q...

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Prof. Stahl 354K Game Theory Problem Set No. 4 Due Feb 10 1) Ronald is indifferent between \$50 for sure and a 25% chance of \$500 or nothing. He is also indifferent between \$25 for sure and a 15% chance of \$500 or nothing. (a) Assuming Ronald's preferences satisfy the axioms of Expected Utility, how would he rank the following three lotteries? Y = {\$500, \$50, \$25, 0} p A = ( .05, .3, .3, .35) p B = ( 0, .75, .1, .15) p C = ( .02, .16, .82, 0) (b) Make up a fourth lottery and compute its utility value U(p). 2) Assume Amy's preferences satisfy the axioms of the expected utility theorem, and consider the following four lotteries: Y = {\$100, \$50, \$20, \$5} p A = ( .4, .1, .4, .1) p B = (.56, 0, 0, .44) p C = (.44, 0, 0, .56) p D = ( .1, .4, .1, .4) . Amy is indifferent between A and B, and she is indifferent between C and D. (a) Without doing any calculations, would Amy prefer A or D, and why? (b) For what value of p would she be indifferent between the lottery
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Unformatted text preview: (p, 0, 0, 1-p) and \$50 for sure? (c) For what value of q would she be indifferent between \$20 for sure and a lottery that pays \$100 with probability q and \$5 otherwise? (d) Make up a fifth lottery and compute its expected utility value. 3) Consider the following four lotteries: Y = {\$400, \$300, \$200, \$100, \$0} p A = ( .75, 0, .25, 0, 0) p B = ( .6, 0, 0, 0, .4) p C = ( 0, 0, .55, 0, .45) p D = ( .35, .18, .15, .2, .12) . Jiong is willing to buy or sell lottery A for \$300, buy or sell lottery B for \$200, and buy or sell lottery C for \$100. [NOTE: A person would be willing to buy or sell an item for \$x if and only that person is indifferent between having the item and having \$x for sure.] Compute the probability α such that Jiong is indifferent between lottery p D and L( α ). 4) Dutta, chapter 27: 19 5) Dutta, chapter 27: 20 6) Plot your preferences on L (Y) = {\$100, \$50, \$0}....
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