Consider the following strategic situation. Two friends are making sushi together. The first friend has offered to go grocery shopping, while the other friend has offered to make the sushi.
?The first friend goes to the supermarket and buys a main ingredient: Tuna, unagi(BBQ eel), or salmon.
?They then buy either avocado or cucumber as a second ingredient. Meanwhile, the second friend has to decide how much sushi rice to make.
?They can either make a large batch or a small batch
?They don't see what their friend has purchased when deciding Finally, they make sushi.
The type of sushi depends on the choices of first friend:
?If they bought cucumber, they make small sushi rolls.
?If they ordered salmon or tuna, and avocado, they make large rolls.
?If they ordered unagi and avocado, they make small rolls.
However, if they make large rolls and have a small batch of rice, they run out. If they make small rolls and have a large batch of rice, they waste some.Both friends value sushi rolls based on their ingredients, and the rice situation:
?Avocado is the best, and is worth 5 utility
?Unagi is the second best, and is worth 4 utility
?Salmon is worth 3 utility
?Tuna is worth 2 utility
?Cucumber is worth 1 utility
?A large roll increases the value by 2 utility
?Running out of rice reduces the value of a roll by 50%
?Wasting rice costs 1 utility.
Payoffs are the sum of all the components. For example, an avocado and salmon bowl with a large amount of rice prepared is worth 5 + 3 + 2 = 10 utility. If they made only a small amount of rice, it would only be worth 5 utility.
(a) (10 points) Draw the tree representation of the game above, being careful to include information sets and actions.(Hint: you might want to re-phrase the first friend's decisions in terms of roll choice,rather than ingredients.)
(b) (10 points) Find any one equilibrium in this game. Explain!(Hint: What possible beliefs can the second friend have?)
(c) (15 points) Draw the matrix representation of your game, and solve it for all of the NE. Which ones agree with your equilibrium? Explain
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