HW5 - Homework Assignment 5 Econ 382 Professor Platt BYU...

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Unformatted text preview: Homework Assignment 5 Econ 382, Professor Platt, BYU Due in class, March 2nd, 2009 1 Warmup Optional questions. Points earned in this section can offset points lost elsewhere (though the maximum score for the assignment is still 100 points). Credit is only given if you show all steps taken to obtain your answer. 1. Bob and Jen are newly married and are just starting to get used to the shared chores around the house. After dinner, it comes time to clean the dishes. If both offer to do the dishes, they work together, the dishes get clean, and each will get 2 utils. If only one offers to do the dishes, that person does the dishes alone and gets -1 util of happiness, while the other relaxes and gets 4 utils. If neither offers, the dishes don’t get clean and they get 0 utils each. (a) (1 pt) Set this up as a normal form game. (b) (2 pts) Solve for the Nash Equilibrium of this game. What is the expected payoffs under that equilibrium? (c) (1 pts) One would hope that this will be a repeated game. If it is only finitely repeated, what will be the equilibrium? (d) (2 pts) Even better, this should be an infinitely repeated game (assuming dishes in the hereafter). Propose an equilibrium strategy that can get a higher av- erage payoff than the finitely repeated game. Then show that it is indeed an equilibrium, provided that Bob and Jen are sufficiently patient. • You should find that with δ > 1 2 , it is better to both offer, with the penalty for a one-time deviation being to never offer again. 2. Suppose that Alex and Bob own the only two firms that refine oil for Utah. Each firm’s product (gasoline) is identical, and consumer demand is given by P = 100- 2 Q ....
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HW5 - Homework Assignment 5 Econ 382 Professor Platt BYU...

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