(i) Write down the maximisation problem that player 2 needs to solve to optimise their own effort, and hence show that Yopt 2+x 4c (ii) Write the maximisation problem facing player 1 in optimising their effort. (iii) Find the Bayes-Nash equilibrium as a function of p for x and y at the two cost values.
(i) Write down the maximisation problem that player 2 needs to solve to optimise their own effort, and hence show that Yopt 2+x 4c (ii) Write the maximisation problem facing player 1 in optimising their effort. (iii) Find the Bayes-Nash equilibrium as a function of p for x and y at the two cost values.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![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 =
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.
(iii) Find the Bayes-Nash equilibrium as a function of p for x and y at the two cost
values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac042761-9e3f-4511-b3d8-b5718b9766e6%2F277a4dcc-8524-40a7-b5d0-565a972f42ca%2Fw4ddhfg_processed.jpeg&w=3840&q=75)
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 =
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.
(iii) Find the Bayes-Nash equilibrium as a function of p for x and y at the two cost
values.
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