3. We consider the following situation between 2 firms. Firm A (the "acquirer") would like to take over firm 7 (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 T; and firm T is worth x (under its 3 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. We consider the following situation between 2 firms. Firm A (the "acquirer") would like to take over firm 7 (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 T; and firm T is worth x (under its 3 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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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P1| P2 Left Middle Right Left 4,2 3,3 1,2 Middle 3,3 5,5 2,6 Right 2,1 6,2 3,3 Consider the simultaneous move game represented by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted, or the discount factor is equal to 1. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a) (Left, Left) is played in both periods. b) (Right, Right) is played in both periods. c) (Middle, Middle) is played in both periods. d) (Middle, Middle) is played in the first period, followed by (Left, Left). e) (Middle, Middle) is played in the first period, followed by (Right, Right).
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1. Assume the payoff matrix for a game is as follows. Firm B X Y Firm A 6,6 14,2 2 2, 14 9,9 What is the maximum interest rate at which collusion could occur between these firms with a trigger strategy if the game is played an infinite number of times?
Q2
Repeated Game Consider the game below, which is infinitely repeated at t = 1,2, .... Both players discount the future at rate d E (0, 1). The stage game is C C 5,5 0,6 D 6,0 1,1 1. The following three questions are about "Grim Trigger" strategies. (a) Describe the "Grim Trigger" strategy profile of this game. (b) Draw the finite automata representation of this strategy profile. (c) Find the lowest value of 8 for this strategy profile to form a subgame perfect equilibrium. 2. Suppose that the players play (C,C) in period t = 1, 3, 5, ... and plays (D,D) in period t = 2,4, 6, ... Compute the discounted payoff of each player. 3. Find a subgame perfect equilibrium such that, on the equilibrium path, (D,D) is played at periods t = 1, 3, 5, ..., and (C,C) is played at periods t = 2, 4, 6, ... Write down the finite automata representation for the strategy profile you proposed. Find the lowest value of d for the profile to form a subgame perfect equilibrium.
a. Consider the game faced by the British and Dutch managers when both are given contracts that compensate them with (1)/(2) of 1% of revenue. The strategic form game is shown. Find the Nash equilibria. b. Now consider the game between the British and Dutch shareholders as to what kind of contracts to give their managers. Assume that they simultaneously choose between a contract that gives the manager 1% of profit and one that gives him (1)/(2) of 1% of revenue. Assume, as before, that the shareholders’ payoff is profit (and we ignore the trivial amount that they pay to their managers). After a pair of contracts is selected, the two contracts are revealed to both managers, and the managers then choose between supply levels of low, moderate, and high. Find all SPNE.
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Suppose the following game is repeated infinitely. The players have a common discount factor & E (0,1). C D 1 C3,2 0,5 D 5,0 1,1 For high enough values of 8, there is an equilibrium of the infinitely repeated game in which (C, C) is played in the first 4 periods followed by (D, D) in sub- sequent periods. Is this true or false? Explain carefully.
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?
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