Prelim2q3 - uz) of utility allocations that constitute the...

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3. (30) Consider the following problem of "dividing a dollar". For player 1, the utility of obtaining Xl is Ul(Xr) Xl, and for player 2, the utility of obtaining Xz is U2(X2) = v'3X2. There is $100 to be split between the two players. If they cannot agree on an equitable split, then each player will receive $0. (a) (8) How would you characterize each player's propensity for risk? p\O\jU \ ;S r~ ~ ~ P I".Y 1,,' s (b) (2) Precisely specify the set of points (Xl, X2) that constitute the bargaining set for this problem. ~ 11 t'0~I1~ (~, I '1. .,) w.e.(.e. . J '- J.. V'Z. ";1)( ~ .. b(CAUst -1tt. vI-,.,. ....... ~~s 1'1.1'\ -Jec.~~ Q4. (c) (8) \Yhat does this bargaining set corJspond to in terms of the utilities of the two players? That is, express the pairs (Ul'
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Unformatted text preview: uz) of utility allocations that constitute the bargaining set for this problem. (Hint: part of your answer is an equation that the pairs (u 1, U2) in the bargaining set must satisfy.) \J -4'~~ '2.-uz. ... ::Jr--"1-2---"3 (v, '\J) ~L ) ... (d) (10) C se the answer to part (c) to find the Nash bargaining so-lution for the problem in terms of a utility allocation for each player. (I think that you will find this part much easier if you use your answer to part (c) in the maximization view of the ~ ash bargaining solution, rather than the (t, r) characterization, but either approach is okay.) (e) (2) Determine the division of the $100 in terms of dollars. 7 , ....
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This note was uploaded on 02/06/2011 for the course ORIE 4350 at Cornell.

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Prelim2q3 - uz) of utility allocations that constitute the...

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