# 3M03_Spring_2008_Test_1_Answers - Econ 3M03 Introductory...

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Econ 3M03 - Introductory Game Theory Answers to Test 1 - Spring 2008 1. Labels: F - Casanova Frankenstein M - Poison the hotdog with mustard P - Poison the plain (without mustard) hotdog A - Captain Amazing B - Eat both hotdogs M - Eat the hotdog with mustard P - Eat the plain hotdog N - Eat neither hotdog ( )( )( )( )( )( )( )( ) M P M M P P BB NN F A 10 10 0 0 10 0 10 0 0 3 ? 0 5 0 ? The question didn't specify what Captain Amazing's payoff was if he ate neither hotdog, so anything in place of the question marks would be fine. (Although I think given the story that it's best if the payoff is between 0 and 3.)

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2. First game: (){ } () { } (){} (){ } 1 1 1 2 2 , , BR X A B RY AB BR Z B BR A X B RB YZ = = = = = There are three pure-strategy Nash equilibria: ( ) ( ) ( ) ,, , , , A XB YB Z . Second game: () { } ( ) { } (){} ( ){} (){} (){} 12 B RL U B RU C B RC M B RM R B RR L B RL L == There are no pure-strategy Nash equilibria. 3. Using as the probability Calvin hides in the ditch and as the probability Suzie looks in the ditch: C P S P ()() () 3 8 04 1 51 1 44 5 1 38 CS SS S S S S uD P uTP PP P P P P = +−= + −=+ = = S P ( ) ( ) 1 2 50 1 14 1 54 4 84 SC CC C C C C uPD uPT P P P P =
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