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…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Required a. Identify three Nash equilibria of this game. b. Explain in words which strategy pair is likely to be played in this game and why. Please give a detailed answer. Thanks!
7. Jane and Joe are a wealthy couple. In part, this wealth is attributable to Jane’s highly successful limousine business. Although Joe has been involved somewhat in the limousine business, he has a variety of other ventures and assets. Jane decides it should be clearly established that she had legal control over the limousine business and how it is run. As a result, the two enter into a contract pursuant to which Jane foregoes all claims to all business ventures in exchange for Joe agreeing to do the same with respect to the limousine business. At the time, the limousine business has an FMV of $2 million and a basis of $500,000. Joe has the equivalent aggregate FMV and basis in his businesses. What are the tax consequences to Jane and Joe respectively?
3. Two parties are bargaining to split the profits from the successful investment. The bargaining has to be settled in five weeks and parties are meeting every week for a round of bargaining. Player 1 makes an offer every odd round and can accept or reject an offer every even round. Player 2 makes an offer every even round and can accept or reject an offer every odd round. The game ends when one of the parties makes an offer the other party accepts, or when the offer is rejected five times (in which case the payoffs of both players are 0). Each round the profits decrease with a discounting factor d .7. a) What distribution of profits constitutes a unique SPNE in this game?
3. We consider the following situation between 2 firms. Firm A (the "acquirer") would like to take over firm T (the "target"). It does not know firm I's value; it believes that this value, when firm T is controlled by its own management, is at least $0 and at most $100, and assigns equal probability to each of the dollar values in this range (we assume that the value is distributed uniformly on this interval). Firm T will be worth 50% more under firm A's management than it is under its own management. Suppose that firm A bids p to take over firm 7; and firm T is worth x (under its own management). Then if T accepts A's offer, A's payoff is 2x-p and T's payoff is p; if T rejects A's offer, A's payoff is 0 and T's payoff is x. (a) Formalize this situation as a Bayesian Game (b) Find the Bayesian Nash Equilibria of this game.
3. Consider the following game in normal form. Player 1 is the "row" player with strate- gies a, b, c, d and Player 2 is the "column" player with strategies w, x, y, z. The game is presented in the following matrix: W x y Z 2,1 0,2 2,1 a 3,3 b 1,1 1,2 1,0 1,4 c 0,0 1,0 3,2 1,1 d 0,0 0,5 0,2 3,1 Find all the Nash equilibria in the game in pure strategies.
3. Consider a two-player, sequential-move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1's actual move and then decides to move right or left. If player 1 moves right, player 1 receives £20 and player 2 receives £45. If both move left, player 1 receives £15 and player 2 receives £30. If player 1 moves left and player 2 moves right, player 1 receives £40 and player 2 receives £40. a. Draw the above situation in the form of an extensive form game. b. Find the sub-game perfect Nash equilibrium of the extensive form game.
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?
6) Assume that Incom Fighter Systems is suing the New Republic for breach of contract. They have filed suit for 100 million galactic credits due to a cancelled X-Wing order. However, before the case goes to trial, the two parties can try and negotiate a settlement. The New Republic can make an offer, and then Incom can either accept the offer or press forward with the suit. (Assume there is just a single offer, and no counteroffers). Each side believes that Incom has a 70% chance of winning the lawsuit if it ends up in court. In addition, Incom would have to pay 15 million credits in lawyers fees, while the New Republic would pay 5 million if the case goes to trial. Draw the game, then solve it to determine its SPNE. What happens? How much does each side end up with?
(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
3. Consider the following game: K Out 2 2 1 9 Player 1 Player 1 X In A Y Player 2 0 2 B 5 5 a) Does the game have perfect information? Why/why not? b) Circle the subgames. c) Find all backward induction solutions. d) Below are written five strategy profiles. One of them is a subgame perfect equilibrium; circle it! One of them is not a Nash equilibrium; write "X" across it! ((Out, X), A) ((Out, Y), A) ((In, Y),B) ((Out, Y), B) ((In, X),B)
3. Repeated Game Consider the game in which the stage game depicted below is infinitely repeated and in which both players discount future payoffs with discount factor 6 € [0, 1]. Player 1 E S Player 2 E 3,3 4, -1 S -1.4 1,1 (a) Suppose that both players play the tit-for-tat strategy. This strategy is characterized by exerting effort (playing E) in the first round. Then in future rounds, a player copies the action chosen by his opponent in the previous period (i.e if Player 2 shirks (plays S) in period 2, then Player 1 plays S in period 3). Then, for what values of d can tit-for-tat be supported on the equilibrium path of play? (b) Suppose that both players play the perfect tit-for-tat strategy. This strategy is characterized by exerting effort (playing E) in the first round. Then in future rounds, a player plays E unless the actions are disagreed in the previous period. Then, for what values of d can perfect tit-for-tat be supported on the equilibrium path of play?
! (asap)

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