QUESTION 5 Player 2 Left P1: $12 P2: $45 P1: $10 P2:$10 Player 2 Left P1: $22 Player 1 Up P2: $22 P1: $26 Down P2:$44 In the game shown above, list all of the EFFICIENT Nash Equilibrium (please check ALL that apply) (up, left) (up, right) (down, left) □ (down, right) No efficient Nash Equilibrium Player 1 List all dominant stragies in the game shown above Up is a dominant strategy for player 1 Down is a dominant strategy for player 1 Left is a dominant strategy for player 2 Right is a dominant strategy for player 2 There are no dominant strategies in this game. QUESTION 6 Up Down Right P1:$50 P2: $0 P1: $35 P2: $3 Right P1:$1 P2: $24 P1: $0 P2: $0

QUESTION 5 Player 2 Left P1: $12 P2: $45 P1: $10 P2:$10 Player 2 Left P1: $22 Player 1 Up P2: $22 P1: $26 Down P2:$44 In the game shown above, list all of the EFFICIENT Nash Equilibrium (please check ALL that apply) (up, left) (up, right) (down, left) □ (down, right) No efficient Nash Equilibrium Player 1 List all dominant stragies in the game shown above Up is a dominant strategy for player 1 Down is a dominant strategy for player 1 Left is a dominant strategy for player 2 Right is a dominant strategy for player 2 There are no dominant strategies in this game. QUESTION 6 Up Down Right P1:$50 P2: $0 P1: $35 P2: $3 Right P1:$1 P2: $24 P1: $0 P2: $0

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 2MC

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Suppose China and the US are deciding whether to join an international agreement to mitigate climate change. The matrix below contains payoffs that represent each country’s net benefit from their decisions. Use this information to answer Question 24. CHINA USA Join Agreement Do Not Join Agreement Join Agreement (100,100) (0,125) Do Not Join Agreement (125,0) (25,25) [24] What does each country decide to do in a Nash equilibrium? AND What is the efficient outcome? Nash: Efficient:
You have just played rock, paper, scissors with your friend. You chose scissors and he chose paper, so you won. Is this a Nash equilibrium? Explain why or why not.
Consider the following dynamic game. There are two players (P1, P2). Player 2 tries to rob Player 1. If Player 1 pays $100, the game is over with Player 1 (victim) paying $100 to Player 2 (robber) (P1: -$100, P2: +$100). If Player 1 refuses to pay $100, then Player 2 has two choices: one is to hurt Player 1 (P1: -$5,000, P2: -$1,000) and the other is to walk away (P1: 0, P2: 0). Explain how to find an equilibrium in this game.
True or false? If a game has a Nash equilibrium, that equilibrium will be the equilibrium that we expect to observe in the real world. False. People don’t always act in the way that a Nash equilibrium requires. People don’t always make the necessary calculations and they take into account the outcome of others. False. A Nash equilibrium is based on very strict assumptions that rarely hold in the real world. No real-world situation leads to a Nash equilibrium. True. As long as people are rational and have their own self-interest at heart, real-life games will result in the Nash equilibrium. True. Nash’s theory of equilibrium outcomes was derived from real-world interactions. The theory holds true for almost all real-world scenarios.
Consider the following game played by four individuals, players 1, 2, 3, and 4. Each individual has $10,000. Each player can donate between $0 and $10,000 to build a public park that costs $20,000. If they collect enough money, they construct the park, which is worth $9,000 to each of them. However, if they collect less than $20,000, they cannot build a park. Furthermore, regardless of whether the park is built or not, individuals lose any donations that they make. a) Describe the Nash equilibria for a simultaneous game. What makes them equilibria? Hint: There are many equilibria, so you may want to use a mathematical expression! b) Suppose that players 1, 2, and 3, each donate $4,000 for the park. How much will player 4 donate and why. What are the resulting payoffs for the players? c) Suppose instead that player 1 donated first, player 2 second, player 3 third, and player 4 last. Furthermore, players could only donate in intervals of 1,000 (0, $1,000, $2,000, etc.). How much will…
If a player does not have a dominant strategy, can the game still have a Nash equilibrium? No. At least one player must have a dominant strategy for the outcome to be a Nash equilibrium. Yes. There is no need for a dominant strategy to exist in order to have a Nash equilibrium. The outcome is a Nash equilibrium because each player has made his or her optimal choice based on the optimal choice of the other player. No. If there is no dominant strategy, there is no predictable outcome and therefore no Nash equilibrium. Yes. A Nash equilibrium is possible only if neither player has a dominant strategy. If a dominant strategy exists, it is no longer a Nash equilibrium.
Two roommates John and Joe are playing a simultaneous game of cleaning the apartment. If neither of them clean, the apartment gets filthy and both get a utility of 2. If John cleans and Joe doesn’t, John gets a utility of 1 and Joe gets a utility of 4. If Joe cleans and John doesn’t, Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment, they each get a utility of 3.What is the Nash equilibrium of this game? Group of answer choices Joe cleans, John doesn’t John cleans, Joe doesn’t Both of them clean the apartment Neither of them clean the apartment
Using game theory, explain why a park in a neighborhood with many long time residents is usually cleaner than a park with many temporary residents. Stick to the econ game theory in your answer. Try to use a payoff matrix box to help describe your answer.
Use the following payoff matrix for a one-shot game to answer the accompanying questions. A 5,5 0, -200 B -200, 0 20, 20 Determine the Nash equilibrium outcomes that arise if the players make decisions independently, simultaneously, and without any communication. Which of these outcomes would you consider most likely? Explain. Suppose player 1 is permitted to “communicate” by uttering one syllable before the players simultaneously and independently make their decisions. What should player 1 utter, and what outcome do you think would occur as a result?
In 2003, Saudi Arabia and Venezuela produced an average of 8 million and 3 million barrels of oil a day, respectively. Production costs were about $10 a barrel and the price of oil averaged $28 per barrel. Each country had the capacity to produce an additional 1 million barrels per day. At that time, it was estimated that each country 1-million-barrel increase in supply would depress the average price of oil by $3. A. Draw a normal form representation of a game where Saudi Arabia has 2 possible actions to produce 8 million or 9 million barrels of oil and Venezuela has 2 possible actions: to produce 3 or 4 million barrels of oil. Fill in the payoffs for each player and action. Draw a table. B. What action should each country take and why? C. Does the asymmetry in the countries' sizes cause them to take different attitudes towards expanding out? Explain why or why not.
Table 15.4, Prisoner Dilemma. Suppose the game starts with both Jesse and Frank planning to “Stay Mum” in the lower right cell. Discuss how each player would evaluate the situation and decide whether to change decisions. If each player makes decisions to minimize the penalty, in which cell will this game end? Is there a Nash equilibrium?
In the following 3-player game, the payoffs represent the number of years in jail. The equilibrium is ________ Group of answer choices Eric and Ned denies. Eric and Tim confess, but Ned denies. Eric confesses, Ned and Tim deny. Eric and Time deny, but Ned confesses