If ExxonMobil invests in Venezuela's oil fields, it runs the risk that Venezuela will later partially nationalize the assets. The payoffs are represented in the game tree illustrated in the figure to the right. Suppose that the parties could initially agree to a binding contract that Venezuela would pay ExxonMobil x dollars if it nationalizes the oil fields. How large does x have to be for ExxonMobil to invest in Venezuela? The value of x would have to be at least equal to $ for ExxonMobil to invest in Venezuela. (Enter your response as a whole number.) Venezuela ExxonMobil Elsewhere Nationalize Government -(24,96) -(60,60) Don't nationalize -(30,0)
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- 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.Suppose OPEC has only two producers, Saudi Arabia and Nigeria, Saudi Arabia has far more oil reserves and is the lower-cost producer compared to Nigeria. The payoff matrix in the table to the right shows the profits earned per day by each country. "Low output" corresponds to producing the OPEC assigned quota and "high output" corresponds to producing the maximum capacity beyond the assigned quota Which of the following statements is true? OA. The Nash equilibrium is a cooperative equilibrium. OB. The Nash equilibrium is a noncooperative, dominant strategy equilibrium OC. The Nash equilibrium is a collusive equilibrium. D. There is no Nash equilibrium in this game because each party. pursues its dominant strategy. Low output Nigeria High output Low output Nigeria earns $20 million Saudi Arabia Nigeria earns $30 million Saudi Arabia earns $100 million Saudi Arabia earns $80 million High output Nigeria earns $12 million Saudi Arabia earns $75 million Nigeria earns $20 million Saudi Arabia…· It was discovered that two domestic manufacturing companies were fixing prices. If each company is silent, there is no penalty, but production and business are disrupted due to continuous investigation by the Fair Trade Commission. The penalty for revealing the estimated loss due to the investigation and collusion is as follows. - Question: Where is the Nash Equilibriur.? Firm 2 Silence Disclosure Silence -100, -100 -680, O Firm 1 Disclosure 0, -680 -470, -470 fine (a hundred million won)
- Suppose O2 and Vodafone are the only two telecommunicationscompanies in UK. Both companies are considering whether ornot to stop offering unlimited data plans. Each company has twostrategies: stop or don’t stop. The first entry in the brackets is the payoffsof O2 and the second entry is the payoffs of Vodafone, both in $million.What will be the dominant strategies of O2 and Vodafone and what willbe the Nash equilibrium? Explain your answers.Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land. Farmer 2 Farmer1 1 cow 2+ cows 1 cow 8,8 2,10 2+cows 10,2 4,4 What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off) The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…Consider the following normal-form game: Player 1 כ M D Player 2 L 4,2 3,7 5,7 8,3 O For Player 1: U and M, for Player 2: C and R For Player 2: U and D, for Player 2: L and C For Player 1: U, M and D, for Player 2: Land C O For Player 1: U and D, for Player 2: C and R 7,9 9,11 R 10,6 9,3 7,8 Which strategies survive iterated elimination of strictly dominated strategies?
- suppose that the world is comprised of two countries: X and Y. Because of the absence of centralized world governance, the control of global externalities is particularly challenging, which is the case with greenhouse gases linked to climate change. The entries in the following Payoff Table describe each country's well-being under different abatement patterns: X\Y No Abate Abate No Abate 12,12 24,8 Abate 8,24 20,20 Now suppose that the game is repeated indefinitely. Define the concepts of Trigger Strategies and also the concept of Business as Usual Strategies for the repeated game. Verify that trigger strategies supporting cooperative payoffs (20,20) constitute a non-cooperative equilibrium of the repeated game when δ=0.8. Are trigger strategies still an equilibrium when δ=0.30? Explain intuitively why and verify that Business as Usual still is an equilibrium in this case.3.1 Do either of the two telecommunications firms have a dominant strategy in this interaction?If so, what are these dominant strategies? 3.2 What is the Nash Equilibrium of the game above? Clearly, show the logic you use to reachyour conclusion. What type of game is this? 3.3 Suppose the two firms could incentivize or punish each other, could the two firms find theirway to the socially optimum outcome? How would they do this? After observing the strategic interaction between Globogym and Average Joe’s, the governmentdecides to pass a law that states that the two terms must pre-commit to the quantities of trainingsessions they will supply to the American market.Market demand for training sessions is still modeled as ? = 400 − 0.2?, as before, and the marginalcost of production is constant at R40 per call. Let the number of sessions provided by Globogym berepresented by ?G and the quantity provided by Average Joe’s be represented by ?A. 3.4 Solve the firms’ reaction functions and…Question 24 In the coordination game shared in class and in the textbook, it shows players Alex and Tyler coordinating over using Microsoft or Apple software. The strategies lead to a situation with two Nash Equilibria where both use Microsoft or both use Apple with each associated with different equal payoffs. This game is illustrating which concept of Network Goods? O The contestability of the market for a network good. O The "best" product may not win. O The coordination amongst competing network goods. O The required scale of success in the market.
- 8. Two states, A and B, have signed an arms-control agreement. This agreementcommits them to refrain from building certain types of weapons. The agreement is supposed tohold for an indefinite length of time. However, A and B remain potential enemies who wouldprefer to be able to cheat and build more weapons than the other. The payoff table for A (player1, the row player) and B (player 2, the column player) in each period after signing thisagreement is below. a) First assume that each state uses Tit-for-Tat (TFT) as a strategy in this repeated game.The rate of return is r. For what values of r would it be worth it for player A to cheat bybuilding additional weapons just once against TFT? b) For what values of r would it be worth deviating from the agreement forever to buildweapons? c) Convert both values you found in parts a and b to the equivalent discount factor dusing the formula given in lecture and section. d) Use the answers you find to discuss the relationship between d and r:…need a good explanation of this, Let G be an impartial game. Prove that G - G = 0 using only that for any game H, o(H) = P if and only if H = 0. important tips: read the instructions carefully and prove it is 0 by showing that second player is winner. o(G)=P iff G=0 use this statement to prove that G- G=0 that yoh can prove it zero by showing that second player is winSolve 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.