Answers Exercise Rotten Kid

# Answers Exercise Rotten Kid - The Rotten Kid Problem 2a)...

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The Rotten Kid Problem 2a) The situation can be modeled as the following extensive-form game: Players : The parents and the child. Terminal histories : The set of sequences ( a , t ), where a is an action of the child and t is a transfer from the parents to the child; a and t are positive numbers. Players’ function : P ( ) is the child, P ( a ) is the parents for each value of a . Preferences : For the child, they are given by: t a c t a U c + = ) ( ) , ( while for the parents, we have: { } t a c t a p t a U p + = ) ( , ) ( min ) , ( 2b) Let us solve the second stage of this game, that is the optimal choice of the parents in terms of transfer t . By assumption, we have: ) ( ) ( a p a c < . Thus, if the parents do not give any transfer, i.e. t =0, then their utility is: { } ) ( ) ( ), ( min ) 0 , ( a c a c a p a U p = = If the parents transfer 1 dollar to the child, then their payment increases by 1 dollar since it is equal to: { } 1 ) ( 1 ) ( , 1 ) ( min ) 1 , ( + = + = a c

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## This note was uploaded on 06/06/2010 for the course ECON 31 taught by Professor Yvez during the Fall '08 term at University of Maine Orono .

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Answers Exercise Rotten Kid - The Rotten Kid Problem 2a)...

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