Doc and Brewster are in a negotiation over royalties. The negotiations proceed as follows. Doc can set a price p. Having seen Doc’s offer Brewster can either accept (A) or reject (R). If Brewster accepts Doc’s offer the payoffs are p to Doc and 500 – p to Brewster. If Brewster rejects (R) the payoffs are 0 to Doc and 30 to Brewster. What is the highest price that Brewster will accept in the subgame perfect equilibrium of this game? p = .
Question
Doc and Brewster are in a negotiation over royalties. The negotiations proceed as follows. Doc can set a price p. Having seen Doc’s offer Brewster can either accept (A) or reject (R). If Brewster accepts Doc’s offer the payoffs are p to Doc and 500 – p to Brewster. If Brewster rejects (R) the payoffs are 0 to Doc and 30 to Brewster. What is the highest price that Brewster will accept in the subgame perfect equilibrium of this game? p = .
Solution
The highest price that Brewster will accept in the subgame perfect equilibrium of this game is 470.
Here's why:
In this game, Brewster will accept Doc's offer if the payoff from accepting is at least as high as the payoff from rejecting. The payoff from accepting is 500 - p, and the payoff from rejecting is 30.
So, Brewster will accept if 500 - p >= 30. Solving this inequality for p gives p <= 470.
Therefore, the highest price that Brewster will accept is 470. If Doc sets a price higher than 470, Brewster will reject the offer and Doc will get a payoff of 0. So, in the subgame perfect equilibrium, Doc will set a price of 470, Brewster will accept, and the payoffs will be 470 to Doc and 30 to Brewster.
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