1. Mali is considering whether to bring a complaint against the Uni...

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1. Mali is considering whether to bring a complaint against the United States before the World Trade Organization about unfair economic subsidies. The United States is deciding how to respond and whether to keep its subsidies. The timing is: 1) Mali decides whether or not to bring the complaint. 2) If Mali does bring a complaint, the United States then decides whether to give in and voluntarily withdraw its subsidies, or resist. 3) If the United States does resist, Mali then decides whether to impose retaliatory trade barriers or not. Such barriers, if imposed, are very costly for both actors. a. Draw a game tree for an extensive game that models the strategic interaction in this situation. Indicate clearly the actor with the choice, as well as the actions available, at each decision node. b. Assign payoffs for both players at all terminal nodes, and justify the preference orderings completely (i.e. explain why these utilities could represent actors' preferences over possible outcomes). c. Find all Nash equilibria (not just subgame-perfect Nash equilibria) of the game, and identify the outcome and payoffs associated with each. Show how you arrive at your answers. 2. The diagram below represents a modified version of Entry-Deterrence. In this version, if players end up at the node (Enter, Fight) a competitive election takes place. Nature randomly chooses the winner of the election. With probability p, Nature chooses the incumbent to win. With probability 1-p, Nature chooses the challenger to win. The value of winning this competitive election is given by the parameter X. C Stay Out Enter I 0,5 Fight Retire N I wins wins 5,0 (p) (1-p) -2,x x,-2 a. For what value (or values) of p is (E,F) an SPNE when: i. x=2 ii. x=7 b. Which value above has a larger range of values of p for which this is a subgame-perfect Nash equilibrium? That is, is (E,F) more likely to be an equilibrum when the payoffs to winning an election are relatively large or when they are relatively small? Explain the intuition of why this is the case in a way a non-game-theorist would understand. Use no more than three sentences. 3. Consider the model of outside options and bargaining power in the UN Security Council. Instead of assuming (as we did in class) that the superpower automatically offers the midpoint between its own and the other actors' ideal point, assume that it is free to offer any policy position x on the continuous interval [0,1] to either actor. The actors have ideal points over the policy space as indicated on the diagram below (and approve of a proposal anytime they are indifferent). The costs for the superpower of excluding the challenger and ally are cC = 0.1 and cA = 0.6, respectively. S NATO A reject reject S S TB TM ou ou SQ rs SQ xs SQ XS XA XC 0.4 0.6 1 a. Will the superpower act unilaterally if it makes a bilateral proposal and is rejected? Will the superpower act unilaterally if it makes a multilateral proposal and is rejected? Explain. b. What is the most favorable policy position for the superpower (i.e. closest to its ideal point) that it can propose in a bilateral offer and induce the ally to accept? What is the most favorable policy position for the superpower (i.e. closest to its ideal point) that it can propose in a multilateral offer and induce the challenger to accept? c. Does the superpower prefer the bilateral accepted offer, the multilateral accepted offer, or some other offer which will be rejected? Explain. d. Given the above, specify precisely the subgame-perfect Nash equilibrium of this strategic interaction, along with the associated outcome and payoffs. 4. Turkey is located at the geographical, political, and economic crossroads between the advanced industrial states of Europe, the affluent oil states of the Persian Gulf, and the looming presence of Russia. As we have seen, this can be a tricky position. Consider its incentives as it decides which relationships to prioritize over the next five years (ignore time thereafter). Building closer relations with the (relatively) steady EU states would have an economic benefit of $8 billion each year over the next five years. Building closer relations with Saudi Arabia and Kuwait would have an economic benefit of $15 billion in the first year, $10 billion in the second year, $5 billion in the third year, and nothing thereafter as oil reserves begin to be exhausted and alternative energy sources grow more prominent. Dealing with Russia is always unpredictable and exciting, so in each period it would be worth $16 billion with probability 0.5 and $2 billion with probability 0.5. a. What is Turkey's ranking in present value of the three deals (i.e. calculate and compare these values) when: i. 8 = 0.9 ii. 8 = 0.6 b. Suppose that, in addition to the benefits of the deal being uncertain in any given period, Turkey is less confident that Russia will continue to honor its terms for the duration. The effect this has is to make Turkey's value of 8 with respect to Russia equal to 0.8, while its value of 8 for the others is 0.9. Which deal is most attractive? 5. South Africa and Botswana are engaged in a strategic interaction governing the prices they will charge on the world market for exports of minerals. Each knows it can capture the entire market (and maximize revenue) by charging a lower price than the other, but if both charge a low price their profits will each be smaller than if both charge a high price. Suppose the game is repeated indefinitely, with a discount factor of 8 and payoffs represented in the game matrix below. a. For what values of 8 will it be an equilibrium for both players to play Tit-For-Tat? b. For what values of 8 will it be an equilibrium for both players to play Grim Trigger? c. If 8 = 0.9 which (or both, or neither) of these strategies is an equilibrium? d. Do any other equilibria exist in this infinitely repeated context when 8 = 0.9? If no, explain why not by arguing why a profitable deviation is guaranteed to exist from any other strategy profile. If yes, explain why there will be (either find one or justify your answer through appeal to a theorem). South Africa High Low Botswana High 4,4 -2,9 Low 9,-2 1,1

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