3M03_All_Tests_Before_Spring_2008

# 3M03_All_Tests_Before_Spring_2008 - Practice Test 1 ECON...

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Practice Test 1 ECON 3M03 Introduction to Game Theory Summer 2003 Each question is worth equal marks. This should take you an hour and fifteen minutes (or less). Vaticrat 1) Suppose, in a particular city, there are two TV stations: channel 1 and channel 2. They have purchased syndicated shows to air each night at 7 p.m. and 7:30 p.m. Channel 1 has purchased Alf and Beverly Hills 90210 . Channel 2 has purchased Cheers and Diffrent Strokes . 10 million people watch one of the two channels at 7 o'clock and 12 million people watch one of the 2 channels at 7:30. Each station must decide which of their two shows to show at 7 o'clock; the other one will then be shown at 7:30. If Alf and Cheers are shown at the same time, one quarter of the audience will watch Alf (and the other three quarters will watch Cheers ). If Alf and Diffrent Strokes are shown at the same time, half of the audience will watch each show. If Beverly Hills and Cheers are shown at the same time, half the audience will watch each show. If Beverly Hills and Diffrent Strokes are shown at the same time, three quarters of the audience will watch Beverly Hills (and the other quarter will watch Diffrent Strokes ). The stations' payoffs are the millions of viewers they attract over the 2 hours. They must simultaneously decide which show to show when. Represent their interaction as an extensive game. What are the strategy sets of the two stations? 2) Consider the following two-player game. Player 1 chooses a number (integer) from 1 to 10 inclusive. Then player 2, who knows the number chosen by player 1, chooses a different number also from 1 to 10. If the two numbers chosen sum to a prime number, then player 1 wins and receives \$1 from player 2. Otherwise (if the sum is not prime) player 2 wins and receives \$1 from player 1. How many different strategies does player 2 have available? (i.e. How many elements are there in player 2's strategy set?) Give an example of one of player 2's possible strategies. 3) For each of the following normal form games, show the best response functions for the two players and find any Nash equilibria. a) Player 2 Y Z A 0 , 0 1 , 1 Player 1 B 0 , 0 0 , 0

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b) Player 2 Y Z A 3 , 2 5 , 1 Player 1 B 2 , 3 3 , 3 c) Player 2 X Y Z A 5 , 1 4 , 3 2 , 2 B 2 , 4 5 , 4 4 , 4 C 3 , 6 1 , 6 3 , 1 Player 1 D 0 , 5 2 , 5 1 , 3 d) Player 2 Y Z A 5 , 3 4 , 4 B 3 , 5 6 , 4 Player 1 C 2 , 1 3 , 7 4) Find the Nash equilibria for the following game. Player 1 chooses a number and player 2 simultaneously chooses a number [ x 1 01 , ] [ ] x 2 , . The payoffs are uxx x 1 1 4 1 3 2 21 1 2 1 2 =+ x and ux x x x 21 2 1 2 2 1 3 2 2 =− .
Test 1 Econ 3M03 – Introduction to Game Theory Spring 2003 Each question is worth 10 marks. Two-part questions are worth five marks for each part. You have one hour and fifteen minutes to write the test. Vaticrat 1) There are two roommates, Xavier and Yassir. In their living room they have three chairs that are three different colours: green, red, and blue. Every night they play the following game.

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3M03_All_Tests_Before_Spring_2008 - Practice Test 1 ECON...

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