Question

1. Suppose you will be playing this game with one other student in the class. Suppose the two of you are traveling to a foreign country. You are carrying identical suitcases and each suitcase contains an identical plate of rare china. Both plates are worth the same amount and only the two of you know their true value. The airline you are traveling on loses both bags. In order to determine an honest appraisal of the value of the plates, each of you is taken to a separate room and asked to write down the value of the plate on a piece of paper as a number between 5 and 15. If both of you write down the same number, the airline will pay both of you that number. Now suppose you write down different numbers. If you wrote down the smaller number, then the airline will pay you an amount equal to the smaller number plus an honesty bonus of 5 points. If you wrote down the larger number than the airline will pay you an amount equal to the smaller number minus a liar's fee of 5 points. Find a Nash equilibrium.

Answer 1

2019 10 Monday lex oth the a players be 1 and 2 si being the amount they wille on the paper i=1,2 vi be the the value of the plate et - Sie [5, 157, P = 1, 2 given. il si = S2 = 5 U (S, 52) = 5 - J = Valls2) | | ka U 18,52) = sirsū , U2 = sq -5 -5 U (s., S2) = Dorost a = S2 +5v 82-5-5

09 Sunday now S,=42=5 , sit [615] can never be a Nash as any player i can bid si-l and get at higher pay off. U (5-1,5) = 5-1+5 l = 5-J+y> 0,15,5) = 5-1 Important Notes

JUNE 11 Tuesday 1 mly 192 sf ů not a Mash 9 AM 10 Up (si, sg) = si-5-T 11 and Us (si, 4) = siū > si sū 12 same reasoning goes foer ergecting Lunch 2 PM 3 now consider, si= 4 = 5 a U, (5,5) = 5V = U2 (5,5) = 5-0 5 U, (6,5) = 5-5-0 =0-5 V =-ū and Ua (56) = 0 a 5-5 Hence, there is no incontine to donate unilaterally ay (55) is a Nash Equrt burim in pure strategy. nportant Notes

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