Harry and Rebecca are working on a joint project. Harry is responsible for the hardware, his choices are between an Apple (A), IBM (B) or Cisco (C). Rebecca will be developing the software choosing between existing software development tools YouCreate (Y) or Zoho Creator (Z). Harry expects her to choose an appropriate software without consulting him. However, YouCreate is incompatible with IBM hardware, but works well with Apple products. Rebecca prefers YouCreate For Apple hardware, otherwise she prefers Zoho Creator. The problem is that Harry has been looking for hardware on his own and has not informed Rebecca which hardware he bought. If Harry bought a Cisco product, it comes with its own software development product. Payoffs are as follows: if Harry bought a Cisco product, they each receive $3, irrespective of the software development tool Rebecca has brought. If Harry bought an apple hardware and Rebecca a YouCreate tool then Rebecca receives $2, and Harry $4. If Rebecca has bought Zoho Creator then Rebecca receives $1 and Harry $2. But if Harry has chosen an IBM product and Rebecca bought a YouCreate development tool, then Harry receives $0 and Rebecca $1. Finally, buying Zoho Creator tool and an IBM product earns Rebecca $2 and Harry $3. Harry knows what choice he will make from {A, B, C) and he chooses first. Rebecca only has a belief that, if Harry discounts Cisco he will choose Apple hardware with probability p. (i) Construct an extensive form game tree for the Bayesian extensive form game de- scribed above, making sure to fully label the graph appropriately. (ii)) Construct the equivalent strategic form game matrix for this extensive form game and find the two Nash equilibria. (iii) Rebecca has a belief of p= 1/4 that Harry will choose Apple hardware. Determine whether she should buy Y or Z.
Harry and Rebecca are working on a joint project. Harry is responsible for the hardware, his choices are between an Apple (A), IBM (B) or Cisco (C). Rebecca will be developing the software choosing between existing software development tools YouCreate (Y) or Zoho Creator (Z). Harry expects her to choose an appropriate software without consulting him. However, YouCreate is incompatible with IBM hardware, but works well with Apple products. Rebecca prefers YouCreate For Apple hardware, otherwise she prefers Zoho Creator. The problem is that Harry has been looking for hardware on his own and has not informed Rebecca which hardware he bought. If Harry bought a Cisco product, it comes with its own software development product. Payoffs are as follows: if Harry bought a Cisco product, they each receive $3, irrespective of the software development tool Rebecca has brought. If Harry bought an apple hardware and Rebecca a YouCreate tool then Rebecca receives $2, and Harry $4. If Rebecca has bought Zoho Creator then Rebecca receives $1 and Harry $2. But if Harry has chosen an IBM product and Rebecca bought a YouCreate development tool, then Harry receives $0 and Rebecca $1. Finally, buying Zoho Creator tool and an IBM product earns Rebecca $2 and Harry $3. Harry knows what choice he will make from {A, B, C) and he chooses first. Rebecca only has a belief that, if Harry discounts Cisco he will choose Apple hardware with probability p. (i) Construct an extensive form game tree for the Bayesian extensive form game de- scribed above, making sure to fully label the graph appropriately. (ii)) Construct the equivalent strategic form game matrix for this extensive form game and find the two Nash equilibria. (iii) Rebecca has a belief of p= 1/4 that Harry will choose Apple hardware. Determine whether she should buy Y or Z.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Harry and Rebecca are working on a joint project. Harry is responsible for the hardware,
his choices are between an Apple (A), IBM (B) or Cisco (C). Rebecca will be developing
the software choosing between existing software development tools YouCreate (Y) or
Zoho Creator (Z). Harry expects her to choose an appropriate software without consulting
him. However, YouCreate is incompatible with IBM hardware, but works well with Apple
products. Rebecca prefers YouCreate For Apple hardware, otherwise she prefers Zoho
Creator.
The problem is that Harry has been looking for hardware on his own and has not informed
Rebecca which hardware he bought. If Harry bought a Cisco product, it comes with its
own software development product.
Payoffs are as follows: if Harry bought a Cisco product, they each receive $3, irrespective
of the software development tool Rebecca has brought. If Harry bought an apple hardware
and Rebecca a YouCreate tool then Rebecca receives $2, and Harry $4. If Rebecca has
bought Zoho Creator then Rebecca receives $1 and Harry $2. But if Harry has chosen an
IBM product and Rebecca bought a YouCreate development tool, then Harry receives SO
and Rebecca $1. Finally, buying Zoho Creator tool and an IBM product earns Rebecca
$2 and Harry $3. Harry knows what choice he will make from {A, B, C) and he chooses
first. Rebecca only has a belief that, if Harry discounts Cisco he will choose Apple
hardware with probability p.
(i) Construct an extensive form game tree for the Bayesian extensive form game de-
scribed above, making sure to fully label the graph appropriately.
(ii)) Construct the equivalent strategic form game matrix for this extensive form game
and find the two Nash equilibria.
(iii) Rebecca has a belief of p = 1/4 that Harry will choose Apple hardware. Determine
whether she should buy Y or Z.
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