Homework 5 Econ 102 Fall 2023

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Swarthmore College *

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Economics

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Feb 20, 2024

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Econ 102 Homework #5 McLeod Due by 11:59pm, Monday, November 13th. Name (please print) __________Alexander Falsone_________________ PSU ID # _________965712919______________________________ Instructions: Please Read Carefully Please download and print out this form. After you have written your answers, scan it and upload it to Canvas. There are 50 possible points on this homework assignment. Late homework will not be accepted!
1. (18 Total Points) Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: Player B Player A Left Right Top 2 6 7 9 Bottom 6 3 4 1 where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B. A) (2 points) Does player A have a dominant strategy, and if so what is it? Player A does not have a dominant strategy. B) (2 points) Does player B have a dominant strategy and if so what is it? Player B does not have a dominant strategy. C) (4 points) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not: i) Top/Left FALSE ii) Top/Right TRUE iii) Bottom/Left TRUE iv) Bottom Right FALSE D) (4 points) For each of the following strategy combinations, write TRUE if it is Pareto
Efficient, and FALSE if it is not: i) Top/Left FALSE ii) Top/Right FALSE iii) Bottom/Left FALSE iv) Bottom Right FALSE E) (2 points) Suppose the game is played where Player A chooses their strategy first. Player 2 observes Player A’s strategy choice, then Player B chooses their strategy. Using the backward induction method we discusses in class, what will be the outcome of the game? (Circle the correct answer.) i) Top/Left ii) Top/Right iii) Bottom/Left iv) Bottom Right F) (2 points) What is Player A’s Maximin Strategy? ______Bottom_____________ G) (2 points) What is Player B’s Maximin Strategy? ______Left____________
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2. (18 Total Points) Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: Player B Player A Left Right Top 2 9 6 10 Bottom 1 11 8 1 where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B. A) (2 points) Does player A have a dominant strategy, and if so what is it? Player A does not have a dominant strategy. B) (2 points) Does player B have a dominant strategy and if so what is it? Player B does not have a dominant strategy. C) (4 points) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not: i) Top/Left FALSE ii) Top/Right FALSE iii) Bottom/Left FALSE iv) Bottom Right FALSE D) (4 points) For each of the following strategy combinations, write TRUE if it is Pareto
Efficient, and FALSE if it is not: i) Top/Left TRUE ii) Top/Right TRUE iii) Bottom/Left TRUE iv) Bottom Right TRUE E) (2 points) Suppose the game is played where Player A chooses their strategy first. Player 2 observes Player A’s strategy choice, then Player B chooses their strategy. Using the backward induction method we discusses in class, what will be the outcome of the game? (Circle the correct answer.) i) Top/Left ii) Top/Right iii) Bottom/Left iv) Bottom Right F) (2 points) What is Player A’s Maximin Strategy? _________________________ G) (2 points) What is Player B’s Maximin Strategy? _________________________
3. (16 points) Suppose a group of cattle ranchers each have $100 to spend. The farmers can either purchase a steer for $100, and let it graze in a common grazing area, or they can buy a bond with the $100 which receives an interest rate of 6%. The table below gives the value of each steer after it has been grazing for one year. # of steers Price per steer Total Value of the Steers Marginal Value of This Steer 1 $132 2 $126 3 $120 4 $114 5 $108 6 $102 a) (12 points) Fill in the two blank columns above. b) (2 points) If the ranchers put their steers in the grazing area one at a time and act only in their self interest, how many steers will be put on the grazing area?
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c) (2 points) If the ranchers work together to maximize their total income, how many steers will be put on the grazing area?