Exam 1 - solutions Pennsylvania State University EXAM 1
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Course
Maths
Institution
Maths
402 Midterm 1
Ron Siegel
Spring 2018
Directions
• Write your name on the exam.
• Exams written with a pencil will not be regraded and cannot be disputed.
• Provide one- or two-sentence explanations when they are requested.
• Complete all problems in the space provided.
• You have ...
exam 1 solutions pennsylvania state university exam 1
402 midterm 1 ron siegel spring 2018 directions • write your name on the exam • exams written with a pencil will not be regraded and cannot be
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402 Midterm 1
Ron Siegel
Spring 2018
Directions
• Write your name on the exam.
• Exams written with a pencil will not be regraded and cannot be disputed.
• Provide one- or two-sentence explanations when they are requested.
• Complete all problems in the space provided.
• You have two sheets of scratch paper. If you need more scratch paper, raise your
hand and one of us will bring it to you.
• Work on scratch paper will not be graded, but everything written on the exam will be
graded. If you need to change an answer, clearly cross out the part you are changing.
• Cell phones and calculators are prohibited.
• You have 75 minutes. The exam ends promptly at 2:50. Five (5) points will be
deducted for every reminder to stop writing.
• There are 4 questions, and 100 points overall.
Name: ______________
• Good luck!
1
, 1. (25 points) Two friends, player 1 and player 2, are about to order food at a restaurant.
The menu includes three dishes: fish, beef, and pasta. Player 1 prefers fish to beef to
pasta. Player 2 prefers pasta to beef to fish. Player 1 orders first, and then player 2
orders. Each player orders one dish. If the dishes the players order differ, then each
player’s payoff is equal to 2 if he orders his most preferred dish, 1 if he orders his
intermediate dish, and 0 if he orders his least preferred dish. Since the players like
to coordinate, if the players order the same dish, each player’s utility is double what
it would be if the other player had ordered a different dish.
Suppose that player 2 observes player 1’s choice before making his choice.
(a) (5 points) Draw the extensive form of this game, labeling all parts and including
players’ payoffs.
(b) (5 points) How many information sets does each player have? How many strate-
gies does each player have? Explain briefly.
Player 1 has one information set and three actions in it. Hence he has three
strategies. Player 2 has three information sets, one for each choice of player
1. In each of his information sets player 2 has three choices. Hence, he has 27
strategies: 3 × 3 × 3.
2
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