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# hw11a - represented by the following payoff matrix Let S =...

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S’11 Prof. Stahl 354K Problem Set No. 11a Due April 21 1. Your local loan agency lends you \$1000, and you must make 12 monthly payments of \$100 each (totaling \$1200), with the first payment in one month. (a) Why is your annual interest rate not equal to \$200/\$1000 = 20%? (b) What is the discounted present value of your payment stream, given a monthly interest rate of r? (c) Find r such that the discounted present value in (b) is exactly equal to \$1000. (d) What is your effective annual interest rate? 2. Give a real world example of (a) a finitely repeated game and (b) an infinitely repeated game. 3. The Game of Chicken . If two drivers keep their throttles to the floor, they both wreak. If one driver "chickens out" first, he is disgraced but lives, while the other is considered a winner. If they chicken out simultaneously, then they both live, neither disgraced nor admired. Assume that living in disgrace is better than dying. These outcomes can be
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Unformatted text preview: represented by the following payoff matrix. Let S = Stubborn and C = Chicken. Assume x > 0 . C S C 1, 1 0, 1+x S 1+x, 0 -1, -1 Find all the one-shot Nash equilibria. 4. Repeated Chicken . Consider the play of the above chicken game twice (assuming the drivers recover from any wreak in the previous play). Use the simple sum of period payoffs. (a) Draw the game tree. (b) Derive the normal form payoffs for at least two strategy profiles. (c) Consider the following strategy. Choose C in the first period. If both players choose the same action (C or S) in the first period, then choose C in the second period with probability 1/(1+x). But if different actions were chosen in the first period, then in the second period choose whatever action you did not choose in the first period (thereby punishing the player who was stubborn). For what values of x is it a subgame perfect Nash equilibrium for both players to use this strategy?...
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