ssume two countries (US and Germany) are facing the decision of whether to participate in the Paris Agreement or not. The following payoff matrix contains e estimated payoffs for both countries for all possible strategies. Germany US Join Not join Join A: (500, 360) C: (450, 300) Not join B: (100, 200) D: (450, 350) What is the Nash equilibrium of this game if it has to be played sequentially and US moves first? O US joins, Germany joins O US joins, Germany does not join OUS does not join, Germany joins

ssume two countries (US and Germany) are facing the decision of whether to participate in the Paris Agreement or not. The following payoff matrix contains e estimated payoffs for both countries for all possible strategies. Germany US Join Not join Join A: (500, 360) C: (450, 300) Not join B: (100, 200) D: (450, 350) What is the Nash equilibrium of this game if it has to be played sequentially and US moves first? O US joins, Germany joins O US joins, Germany does not join OUS does not join, Germany joins

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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Assume two countries (US and Germany) are facing the decision of whether to participate in the Paris Agreement or not. The following payoff matrix contains the estimated payoffs for both countries for all possible strategies. Germany US Join Not join Join A: (500, 360) B: (100, 200) Not join C: (450, 300) D: (450, 350) What is the Nash equilibrium of this game if it has to be played sequentially and US moves first? US joins, Germany joins US joins, Germany does not join US does not join, Germany joins US does not join, Germany does not join
Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.
Consider trade relations between Canada and Mexico. Assume that the leaders of the two countries believe the payoffs to alternative trade policies are as follows: Canada High Tariffs Low Tariffs Mexico High Tariffs Canada trade value = $65 Mexico trade value = $75 Canada trade value = $35 Mexico trade value = $285 Refer to Table 17-4. When this game reaches a Nash equilibrium, what will the value of trade flow benefits be? Canada $35 and Mexico $285 Canada $65and Mexico $75 Canada $130 and Mexico $5 Low Tariffs Canada trade value = $140 Mexico trade value = $5 Canada trade value = $130 Mexico trade value = $275 Canada $140 and Mexico $275
ALBUS MINERVA N S Z MINERVA لی a C a b 3,3 ALBUS b 0,4 2,2 4 N S 15,2 1,3 13,1 For the above sequential game, both Albus and Minerva make moves in two possible situations. A number in purple indicates which node of the two for each of Albus and Minerva. Albus' strategy NS indicates a strategy of taking action N at node 1 and action 5 at node 4. Minerva's strategy ab indicates a strategy of taking action a at node 2 and action b at node 3. Adopt this format of writing strategies, find the subgame perfect Nash equilibrium. Fill in the blanks: The subgame perfect Nash equilibrium of this game is "Albus" Minvera"
on Mary, UE, BD UF, AC DF, BC UF, BD DE, AC DE, BC Nancy U D Nancy -5,4 Mary -0,2 -6,2 -2.6 Which of the following answers is a subgame perfect Nash equilibrium in this game? Check all that apply. (Answers below are formatted as Mary's strategy, Nancy's strategy.)
Consider the following simultaneous game: Player 1 U D Player 2 L 20,-10 -10, 20 R -10, 20 20,-10 Please indicate whether each of the following statements is true or false. Player 1 has a dominant strategy. This game has a Nash equilibrium. This game has a Nash equilibrium in pure strategies. Player 1's best response is D if player 2 plays R.
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:
2. Consider two players playing a simultaneous moves game. These players can be one of the two states of the world, state 1 or state 2, while playing the game. The payoffs-matrix for the two state games are as follows: State 1 P1 U D P2 L R 1,4 1,0 1,6 2,16 0,0 0,24 M State 2 P1 U D P2 L M R 1,0 1,4 1,6 2,16 0,24 0,0 Each players believes that the two states are equally likely, Derive the BNE of the game.
When you are with a young child and want to show them something fun and new, there is the risk that, if they enjoy it, they'll ask for it over and over and over again, and if you ever say no they'll throw a fit, which you will then have to deal with. Consider the following game: First, you decide whether to show them an Old thing again, or a New thing. If you show them the Old thing, you get 2 points and the kid gets 2 points Then, If you showed them the New thing, the kid chooses whether to Ask for it to happen again, or Not Ask. If they choose Not Ask, you get 3 points and the kid gets 3 points If they choose to Ask, you can choose to say Yes, in which case you get 1 point and the kid gets 4 points, or No, in which case they throw a fit, and you get 0 points and the kid gets 2 points Draw the game tree for this game.
What is the Nash equilibrium in this game? In the Nash equilibrium both Saudi Arabia produce a low output and earn a profit of $100 million and $20 million respectively. In the Nash equilibrium both Saudi Arabia produce a high output and earn a profit of $60 million and $20 million respectively. In the Nash equilibrium Saudi Arabia produces a low output and earns a profit of $80 million and Nigeria produces a high output and $30 million respectively. There is no Nash equilibrium.
Consider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?
2. Paul and Stella play a game with three strategies each, T, M, and B for Paul, and L, C, and R for Stella. Both move simultaneously. The payoffs are given by the following form: Stella L с R Paul T (8,4) (10, 2) (2,3) M (4,2) (10, 1) (5,7) B (1,4) (10, 3) (9,-4) a. Which strategy is dominated? b. What is the pure-strategy Nash equilibrium? Identify all if there are more than one. c. If Paul moved first, so that Stella observed it, which strategy would Paul choose?