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(d) Here Alice is fixed on 1 hat, meaning that we must restrict our choices to the top 2 squares. Of those, Bob's optimal choice lies on the upper right square, where he makes 2 hats.
(e) The process here is the same as before, but now since Alice is fixed on two hats, we focus on the bottom squares. The value where B is highest is on the bottom right square, and would be Bob's best response.
(f) Now we flip the scenarios. If Bob is fixed on making 1 hat, then we focus on the left column. Alex's optimal choice is located on the bottom left square.
For when Bob makes 2 hats, we look to the right column. Alice's optimal choice is now located on the bottom right sqaure.
(g) Regardless of who chooses first, the other is going to fall to the sqaure where they can make 2 hats.. What this means is that in the end they will decide upon the bottom right square,. Here they both will be maximizing their profit since both are able to sell two hats rather than one.
Please let me know if you need any clarification. I'm always happy to answer your questions.
Nov 20th, 2015
Dec 19th, 2015
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