3. (40 points) As fall is upon us, consider two individuals, Alyssa and Zhenxun, who are thinking about going to Deep Creek Lake this coming weekend. If they go to Deep Creek Lake and it does not rain, their utility is 100. If they go to Deep Creek Lake and it does rain, their utility is -200. If they do not go, their utility is 0. Alyssa does not listen to the weather, but instinctually "knows" that there is a 20% chance of rain, and an 80% chance of no rain. (a) (10 points) Of the models we have discussed on ambiguity, which model best describes Alyssa's behavior? Briefly explain. (b) (10 points) Using the model you chose, will Alyssa want to go to Deep Creek Lake this weekend? Zhenxun listened to two weather forecasts, which give the following probabilities. He is ambiguity averse. Rain Don't Rain. P 0.6 p' 0.5 0.4 0.5 (a) (10 points) Will Zhenxun want to go to Deep Creek Lake this weekend? (b) (10 points) Assume that Zhenxun already booked a trip out to Deep Creek Lake, and is considering selling his hotel reservation to Alyssa. Is there a price that Zhenxun is willing to sell his reservation and Alyssa is willing to buy it? (c) (+5 bonus points) Again, assume that Zhenxun already booked a trip out to Deep Creek Lake, and is considering selling his hotel reservation to Alyssa. Is there a price that Zhenxun is willing to pay Alyssa to take his reservation and Alyssa is willing to be paid to accept it?