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solution11a

# solution11a - Econ 354K Game Theory Solutions to Problem...

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Econ 354K Game Theory Solutions to Problem Set No. 11a 1. Loan (a) It’s because you do not have \$500 for the full year. You make monthly payments. (b) 13 0 12 10 1 3 13 12 12 1 11 1 1 1 1 55 55 55 1 1 1 1 1 1 ( 1 ) 55 1 55 55 nn n n r rr r r r r r r r r ∞∞ == = ⎛⎞ ⎜⎟ ⎡⎤ + ⎝⎠ =− = ⎢⎥ ++ + + ⎣⎦ −− + = = ∑∑ (c) monthly interest rate: 12 1( 1 ) 55 500 4.55% r r r −+ =⇒ (d) effective annual interest rate: (1+r) 12 -1 70.6% 2. Give a real world example (a) a finitely repeated game and (b) an infinitely repeated game. 3. The Game of Chicken: S – stubborn; C – chicken; x > 0 C S C 2,1 0,2+x S 2+x,0 -3,-3 (a) One-shot Nash equilibria: Pure-strategy NE: (S,C) and (C,S) Mixed-strategy NE: p i =(3/(3+x), x/(3+x)), i=1,2 (for both players). It yields an expected utility of 6/(3+x). (b) (-3, -3) (0, 2+x) (2+x, 0) U 2 U 1 (2, 2) minimax (0, 0)

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4. Two Period Chicken. (b) E.g. strategies CCS** and S*C*C would go from 1.1 to the left side of 2.1, hence to 1.3 (and 2.3),and at this second period player 1 chooses S while
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solution11a - Econ 354K Game Theory Solutions to Problem...

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