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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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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