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.

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 5PA

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