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HW3-answer - Dr Huanxing Yang Econ 601 Game Theory Homework...

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Dr. Huanxing Yang Econ 601 Game Theory Homework Assignment 3 Due April 23, Wednesday 1. Chapter 5, Problem 5 a) The payoff matrix is shown in Figure SOL5.5.1. There is a unique Nash equilibrium in which both order salmon. In fact, salmon is the dominant strategy. Note that they're worse off than if they could both somehow agree to order pasta. Figure SOL5.5.1 - Dining game with two players Diner 2 7.00, 7.00 3.50, 8.50 -1.00, 7.00 Diner 1 8.50, 3.50 5.00, 5.00 0.50, 3.50 7.00, -1.00 3.50, 0.50 -1.00, -1.00 Pasta Salmon Filet Mignon Pasta Salmon Filet Mignon b) Note that a diner cannot influence what others order and thus must pay 25% of the price of the meals they order. All that a diner can influence is what she orders. The key property to note is that whatever she orders, she only pays 25% of the price with the remaining 75% being paid by the other three diners. Once recognizing that this is the actual cost to her, not the price on the menu, a diner should choose the meal that maximizes her surplus. Taking all this into account, Table SOL5.5.2 shows the cost faced by a diner. For example, a diner who orders the pasta dish only pays 25% of it which is $3.50. We observe that each diner orders the filet mignon because it really only costs them $7.50 and the surplus is maximized with that order. The unique Nash equilibrium is then that all four diners order the steak. Hence, each gets a meal they value at $29, but end up paying $30! Table SOL5.5.2 Dish cos Pr $21.00 $3.50 $17.50 $26.00 $5.25 $20.75 $29.00 $7.50 $21.50 Value Actual t Surplus Pasta imavera Salmon Filet Mignon 2. Chapter 5, Problem 10 First note that one Nash equilibrium is the strategy profile in which all citizens choose
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