Bayesian Nash Equilibrium

Firm A is considering taking over firm B. It does not know firm B?s value; it believes that this value, when firm B is controlled by its own management, is at least ?0 and at most ?150, and assigns equal probability to each of the 151 euro values in this range. Firm B knows its own value. Firm B will be worth 50% more under firm A?s management than it is under its own management. Suppose that firm A bids ? to take over firm B, and firm B is worth ? (under its own management). Then if B accepts A?s offer, A?s payoff is (1.5? ? ?) and B?s payoff is ?; if B rejects A?s offer, A?s payoff is 0 and B?s payoff is ?. Model this situation as a Bayesian game with simultaneous moves in which firm A chooses how much to offer and firm B decides the lowest offer to accept. Find the Bayesian Nash equilibrium (equilibria) of this game.

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