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1. Now Suppose that the Fed targets the interest rates. In response to any shooks, it adjusts the money supply to mentain the interest rates at its minal targeted level! How will this interest rate targeted strategy affects the vanations of output from the full employment - level under fuch of the two types of shocks ? 2 17 the only source of shocks money in the economy I autonomous Investment spending, should the Fed stick to many or interest rates targets to best stabilize GDPP 3. Assume that in the Shortrun, there are two types of Shocks Which may cause the level, of GDP to deviate from The longnen, full employment level: () Changes in autonomous investment Spending and (21 Changes in autonomous money demand. Explain how you reached your results for all parts of this questions . Use graphs 4. Suppose that players A and B play the rock paper Scissors / game / paper wins over rock, scissors wins over paper, rock wins over scissors, and draw for any matching pair) Denote by S. ISBy ( r, ps ) the set of strategies, respectively for both players in each game, which responds to rock, paper, and scissors respectively . "Suppose that player A wes mixed strategy PA= (0.1, 012, 0.7 Where each number Is the probability of rock, paper or scissors respectively, Suggest a winning mixed strategy for player B. Use the expected pay off to prove that The strategy Is winning .ECONOMICS 3014: GAME THEORY Answer any THREE questions. All questions curry equal weight, In cer where a student areovers more questions than requested by the canmination rubric, the policy of the Economica Department is that the atu- dents first set of answers up to the required number will be the ones that count (not the best anwars). All remaining answers will be ignored 1 a) Consider a game in strategic form, G. Define a strictly dominated strategy. Suppose that player i has a strictly dominated strategy , Explain why s, cannot be played in any jure strategy Nash equilibrium of the game G. Explain also why s cannot be played with positive probability in any mixed strategy Nash equilibrium of G. b) Consider the game with payolls as depicted in the table below. Player 1 in the row player and her payoff in written first in every cell, and player 2 is the column player. 0.3 6.2 8.4 Eliminate the strictly dominated strategies for each player. Solve for all the pure strategy Nash equilibria of the mune. Solve for a mixed strategy Nash equilibrium, where each player randomizes bet you two of his pure strategies, 2. Consider a homogeneous good oligopoly with 2 finus, where the market price P(Q) = 100 - Q, with Q = gu + 9. (q , the quantity produced by firm (. E a non-negative mal number) Both firma have zero costs. Firm I seeks to maximize profits, Le. P(Q)gi. Firm 2 is unconcerned about profits; Instead it socks to miniman the (absolute) difference between its own output and that of firm 1. That is, firm 's payoff is given boys V(one)= -(91-4): a) Draw a diagram to deplet the beit response functions of the two firms, Lo, firm I's best mapone as a function of ge, and firm 2's best response as a function of gi Salve for a pure strategy Nash equilibrium of the game where the firms choose quantithe (q) sinaitancously. b) Solve for the subgame perfect equilibrium of the game when firm I chooses q1. Firm 2 observes firm I's choice and chooses o. Explain why firm 1 has an incentive to choose differently in this equilibrium from the way it choous in part. (a). c) Solve for the subgame perfect equilibrium of the game where firm 2 moves first and chooses of. Finn I obeerves firm 2's choice and choose ?). ECON3014: TURN OVER 3. Consider an maction for a single indivisible good with two bidders, (1.2), mid private values. Each bidder's valuation of is independently and uniformly distributed on the interval [1.2), and this is common knowledge among the players, A bidder observes his own valuation, but at the valuation of his oppo- ment. Consider a smiled bid first price auction, where the object in allocated to the highest bidder, and the price that this bidder pays is equal to his own bid. (Rocall that if a random variable a is uniformly distributed on the interval [a.a + 1]. then the olf F() = r- a k rep,a+ 1]) a) Suppose that bidder 1 areunus that bidder 2's bid is a linear and strictly Increasing function of her valuation. That is be resumes that by(e,) =a + fey, where a and a are constants; A > 0. Write down the expected payoff to bidder 1. as a function of his own valuation and his bid. (Ignore ties, where both bidders bid the same amount.) Maximize this expected payoff to solve for bidder I's optimal bid, as a function of his valuation. b) Use your results in (a) to solve for a symmetric Bayes Nash equilibrium, Le. one where both hidden bid the same linear function of their valuations, i.. where a mid d are the same for both bidders