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0 Two companies, player 1 and player 2, must decide how much time to devote to a joint project. If player 1 contributes r > 0 hours and player 2 contributes y > 0 hours then the value of the project to the companies is x+ y+ xy/2. The contribution of the two companies come at different costs: (1) Contributing x costs player 1 a?/2; (b) contributing y costs player 2 cy? where c= 1/2 or c= 1. Player 2 knows the value of c but player 1 does not. Player 1 believes that c = 1/2 with probability p and c =1 with probability 1 – p. (i) Write down the maximisation problem that player 2 needs to solve to optimise their own effort, and hence show that 2+ x Yopt = 4c (ii) Write the maximisation problem facing player 1 in optimising their effort.

0 Two companies, player 1 and player 2, must decide how much time to devote to a joint project. If player 1 contributes r > 0 hours and player 2 contributes y > 0 hours then the value of the project to the companies is x+ y+ xy/2. The contribution of the two companies come at different costs: (1) Contributing x costs player 1 a?/2; (b) contributing y costs player 2 cy? where c= 1/2 or c= 1. Player 2 knows the value of c but player 1 does not. Player 1 believes that c = 1/2 with probability p and c =1 with probability 1 – p. (i) Write down the maximisation problem that player 2 needs to solve to optimise their own effort, and hence show that 2+ x Yopt = 4c (ii) Write the maximisation problem facing player 1 in optimising their effort.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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O Two companies, player 1 and player 2, must decide how much time to devote to a joint project. If player 1 contributes x > 0 hours and player 2 contributes y > 0 hours then the value of the project to the companies is x + y + xy/2. The contribution of the two companies come at different costs: (1) Contributing x costs player 1 a? /2; (b) contributing y costs player 2 cy² where c = 1/2 or c = 1. Player 2 knows the value of c bụt player 1 does not. Player 1 believes that c = probability p and c= 1 with probability 1 – p. 1/2 with (i) Write down the maximisation problem that player 2 needs to solve to optimise their own effort, and hence show that 2+ x Yopt 4c (ii) Write the maximisation problem facing player 1 in optimising their effort.
Transcribed Image Text:O Two companies, player 1 and player 2, must decide how much time to devote to a joint project. If player 1 contributes x > 0 hours and player 2 contributes y > 0 hours then the value of the project to the companies is x + y + xy/2. The contribution of the two companies come at different costs: (1) Contributing x costs player 1 a? /2; (b) contributing y costs player 2 cy² where c = 1/2 or c = 1. Player 2 knows the value of c bụt player 1 does not. Player 1 believes that c = probability p and c= 1 with probability 1 – p. 1/2 with (i) Write down the maximisation problem that player 2 needs to solve to optimise their own effort, and hence show that 2+ x Yopt 4c (ii) Write the maximisation problem facing player 1 in optimising their effort.
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