Apple and Google are interested in hiring a new CEO. Both firms have the same set of final candidates for the CEO position: Indra, Cao, and Virginia. Both firms need to decide who to make a job offer to, and the hiring process is such that they each only make one job offer. If, say, Apple makes a job offer to Indra and Google makes a job offer to one of the other candidates, then Apple’s probability of success in hiring Indra is pIndra. The same is true for Google. If they both make a job offer to Indra, each has probability pIndra/2 of success. It has been estimated that pIndra = 20%, and pCao = pVirginia = 30% (Note that these probabilities need not add up to 100%).
Apple and Google are interested in hiring a new CEO. Both firms have the same set of final candidates for the CEO position: Indra, Cao, and Virginia. Both firms need to decide who to make a job offer to, and the hiring process is such that they each only make one job offer.
If, say, Apple makes a job offer to Indra and Google makes a job offer to one of the other candidates, then Apple’s probability of success in hiring Indra is pIndra. The same is true for Google. If they both make a job offer to Indra, each has probability pIndra/2 of success. It has been estimated that pIndra = 20%, and pCao = pVirginia = 30% (Note that these probabilities need not add up to 100%).
Suppose that both Apple and Google attach a valuation of 10 to successfully hiring Indra, and a valuation of 7 to successfully hiring each of the other candidates. A hiring attempt, if unsuccessful, has a valuation of zero.
- Convert this story into a game by completing the following game table;
|
|
|
|
|
|
|
Indra |
Cao |
Virginia |
Apple |
Indra |
(1, 1) |
|
|
|
Cao |
|
|
|
|
Virginia |
|
|
(1.05, 1.05) |
Find any (pure-strategy) Nash equilibria in the game
![2. Apple and Google are interested in hiring a new CEO. Both firms have the same set of final
candidates for the CEO position: Indra, Cao, and Virginia. Both firms need to decide who to
make a job offer to, and the hiring process is such that they each only make one job offer.
If, say, Apple makes a job offer to Indra and Google makes a job offer to one of the other
candidates, then Apple's probability of success in hiring Indra is Rlndta. The same is true for
Google. If they both make a job offer to Indra, each has probability ploda/2 of success. It has
been estimated that plndca = 20%, and pcag = Rviczioia = 30% (Note that these probabilities need
not add up to 100%).
Suppose that both Apple and Google attach a valuation of 10 to successfully hiring Indra, and a
valuation of 7 to successfully hiring each of the other candidates. A hiring attempt, if
unsuccessful, has a valuation of zero.
(a) Convert this story into a game by completing the following game table;
Google
Indra
Cao
Virginia
Apple
Indra
(1, 1)
Cao
Virginia
(1.05, 1.05)
(b) Find any (pure-strategy) Nash equilibria in the game.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9f2f1d5-505b-4ade-b0f8-1616ac0c8b38%2Fd26b9d26-9524-4558-86ce-1863df581324%2F9llt4wn_processed.jpeg&w=3840&q=75)
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