3. (Infinitely Repeated Game). Two banks are competing for loans from clients.They compete through charging different interest rates (e.g. 4%, 6%, and 8%).The amount of loans (in million pesos) that each bank secures and thecombination of interest rates are shown in the payoff matrix belowBank 24%6%8%Bank 14%0,02, 14, -16%1,24,47,18% -1,41,75,5a. What is the pure strategy Nash equilibrium if this game is played once?b. Can cooperation (i.e. both banks charging 8% and earning 5 million pesoseach) be sustained as a subgame perfect nash equilibria (SGPNE) through thefollowing trigger strategy?ornotAt t=1: Cooperate by charging 8%In period t>1: Charge 8% if both banks charged 8% in the previous period,charge 6% forever if one or both banks in all previous periods didcharge 8%c. Consider now the following strategy (Temporary punishment in the TriggerStrategy):period,At t=1: Cooperate by charging 8%In period t>1: Charge 8% as long as both banks charge 8% in the previousperiod. If one of the banks did not charge 8% in the previouscharge 6% for three periods then return to 8% afterwards.

The Prisoner's Dilemma That Is Repeated IndefinitelyA Prisoner's Dilemma situation that can be…

Answered: 3. (Infinitely Repeated Game). Two…

Principles of Macroeconomics (MindTap Course List)

7th Edition

ISBN:9781285165912

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter14: The Basic Tools Of Finance

Section: Chapter Questions

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4. Consider the following model of a bank run. Depositors may either Hold or Withdraw their funds from a bank. Both players hold deposits of 6, which earn interest of 1 if kept in the bank. If either depositor withdraws then the bank fails. If both try to withdraw then each depositor can only recover half of their deposits. The payoffs for a two-player version of this game are given below: Player 2 Player 1 Hold Withdraw Hold 7,7 6,0 Withdraw 0,6 3,3
43. On June 1, you win $1 million in a lottery and imme- diately acquire numerous "friends," one of whom offers you the deal of a lifetime. In return for the million, she'll pay you a cent today, two cents tomorrow, four cents the next day, eight cents the next, and so on, stopping with the last payment on June 21. (a) Assuming you take this deal, how much money will you receive on June 21? (b) Should you take the deal? Explain. (c) Would you take the deal if payments continued for the entire month of June?
4. You have just won a Casino Jackpot prize of $1,000,000 collectable in 10 yearly installments of $100,000 starting today. a) Why is this prize not really $1,000,000? b) What is it really worth today if money can be invested at 10 percent annual interest, compounded monthly?
9. Find all of the Nash equilibria for the three-player game here. Player 1 a b Player 3: A Player 2 X y Z 1,1,0 2,0,0 2,0,0 3,2,1 1,2,3 0,1,2 2,0,0 0,2,3 3,1,1 Player 1 a b C Player 1 Player 3: C X Player 2 y 2,0,0 0,1,2 0,1,1 1,2,1 3,1,2 0,1,2 a b C Player 3: B Player 2 X 2,0,0 1,2,0 0,1,2 Z 0,1,2 0,1,2 1,1,2 y 0,0,1 1,2,1 2,2,1 Z 2,1,2 1,2,1 2,1,0
4. Consider the game matrix below. A company is thinking about establishing itself in a market. Another company is already in this market and can choose to start a price war or not. Company 1 can thus choose "Establish" or "Do not establish"; company 2 "Price war" or "Nothing price war". The numbers in the cells are profits (in thousands of SEK). In each cell, company 1's profit is listed first: (100,60) thus means that company 1 receives one hundred thousand SEK in profit and that company 2 receives sixty thousand SEK in profit. Both firms are profit maximizing. 4a Företag 2 Priskrig Inget priskrig Etablera (100, 60) (120, 25) Företag 1 Etablera ej strategy. Motivate based on the gains i game matrix. (170, 50) (80, 90) Analyze whether company 1 has a dominant the 4b Analyze whether company 2 has a dominant strategy. Motivate based on the gains i the game matrix. 4c. Determine all Nash equilibria of the game. Justify based on the winnings in the game matrix
7) The following payoff matrix shows the annual profits of Target and Costco if they choose different combinations of advertising strategies. The payoff of Costco is listed first, and the profit of Target second. Use the given payoff matrix to answer questions 8 to 12. TABLE 24 Costco O Spend $1B on advertising OO Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B Does Costco have a dominant strategy? If yes, what is it? $4.2; $2.2B Costco does not have a dominant strategy. Yes, the dominant strategy is to spend $1B on advertising. Yes, the dominant strategy is to spend $1.5B on advertising. It cannot be determined. Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3B
6. (a) For the following extensive-form game: 1. Identify the pure and mixed strategy Nash Equilibria ii. Is the set of pure and mixed strategy Subgame Perfect Nash equilibria of the game different from the set of equilibria identified in part (a)? Explain (a couple of sentences should suffice). (3,1) A Player 1 a a2 D (-2,-2) 2 Player 2 b₁ b₂ 3,0 0,1 2,1 2,1 B с (2,5) D (b) Consider the simultaneous-move game below with two players, 1 and 2. Each player has two pure strategies. If a player plays both strategies with strictly positive probability, we call it a strictly mixed strategy for that player. Show that there is no Nash equilibrium in which both 1 and 2 play a strictly mixed strategy. (0,7)
Problem 07-16 (algo) Suppose Fiat recently entered into an Agreement and Plan of Merger with Case for $4.3 billion. Prior to the merger, the market for four-wheel-drive tractors consisted of five firms. The market was highly concentrated, with a Herfindahl-Hirschman index of 3,100. Case's share of that market was 20 percent, while Fiat comprised just 14 percent of the market. If approved, by how much would the postmerger Herfindahl-Hirschman index increase? Based only on this information, is the Justice Department likely to challenge the merger according to the Horizontal Merger Guidelines? No Yes O Possibly - but other factors will be considered
1. Suppose that you are in charge of purchasing for a U.S. corporation that is planning to acquire a large number of new computers. The company's computer specialist has identified two models, one Japanese-made and one U.S.-made, that meet the necessary specifications. Since the two models are essentially equivalent, the company will buy the one with the lower price. Suppose the U.S.-made computer costs $2,400, and a similar Japanese-made computer costs 242,000 yen. If the nominal exchange rate is 110 yen per dollar, which computer is a better buy? (Hint: calculate the real exchange rate for computers)
2. (Based on Roy Gardner, Games for Business and Economics) Two competing firms are deciding how much to invest in advertising. They can choose a low budget (L) or a high budget (H). The payoffs are as follows: L H L 100, 100 120, 40 H 40, 120 60, 60 What is the solution to this game? How does this game resemble the Prisoners' Dilemma?
2. (17) Bob and Joe both own convenience marts on opposite corners. Both firms are considering expanding the size their stores. The payoff matrix for this decision is shown below. Does Bob's Mart have a dominant strategy? Explain why or why not. Expand Bob's Mart Strategy Joe's Expand Mart Strategy Don't Expand Bob's profit $-1,000 Joe's profit=$-1,000 Bob's profit $10,000 Joe's profit=$-2,000 Don't Expand Bob's profit $-2,000 Joe's profit $10,000 Bob's profit $15,000 Joe's profit=$5,000 = 3.Suppose that an industry contains only four firms. The table below shows the market share of each firm in the market. Percentage Share of: Firm A 25 Firm B 30 Firm C 15 Firm D 30 (16) Calculate the Herfindahl-Hirschman index for the industry. In which category would regulators consider this industry base on the index?
(9) Solve the following three-stage game through backwards induction. 1 L R 2 L R L R L/ 1\R L/ 1\R L/1\R L/1\R 1,0 -1,3 0,1 -1,0 1,2 2, 1 0,1 -3,4

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