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 50 – p to Brewster. If Brewster rejects (R) the payoffs are 20 to Doc and 40 to Brewster. With respect to the subgame perfect equilibrium, which statements are true?Group of answer choicesDoc offers a price of p = 10Brewster rejects the offer he gets in equilibriumBrewster accepts the offer he gets in equilibriumBrewster accepts any offer of p ≥ 40.Doc offers any price greater than or equal to 20Doc offer a price less than or equal 40
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 50 – p to Brewster. If Brewster rejects (R) the payoffs are 20 to Doc and 40 to Brewster. With respect to the subgame perfect equilibrium, which statements are true?Group of answer choicesDoc offers a price of p = 10Brewster rejects the offer he gets in equilibriumBrewster accepts the offer he gets in equilibriumBrewster accepts any offer of p ≥ 40.Doc offers any price greater than or equal to 20Doc offer a price less than or equal 40
Solution
In the subgame perfect equilibrium, the following statements are true:
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Brewster accepts the offer he gets in equilibrium: This is true because in a subgame perfect equilibrium, players play optimally in every subgame. This means that Brewster, knowing that rejecting the offer would give him a payoff of 40, will accept any offer where he gets more than 40.
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Doc offers a price less than or equal to 40: This is true because Doc knows that Brewster will reject any offer where he gets less than 40. Therefore, in order to ensure that Brewster accepts his offer, Doc will offer a price where Brewster's payoff (50 - p) is at least 40, which means that p must be less than or equal to 10.
The other statements are not necessarily true in the subgame perfect equilibrium. Doc would not offer a price of p = 10 because this would give Brewster a payoff of 40, which he could also get by rejecting the offer. Therefore, Doc has an incentive to offer a slightly higher price to ensure that Brewster accepts. Similarly, Brewster would not accept any offer of p ≥ 40 because this would give him a payoff of less than 40, which is less than what he could get by rejecting the offer. Finally, Doc would not offer any price greater than or equal to 20 because this would give Brewster a payoff of less than 30, which is less than what he could get by rejecting the offer.
Similar Questions
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