Two travelers buy identical handcrafted souvenirs and pack them in their respective suitcases for their return...

 

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Two travelers buy identical handcrafted souvenirs and pack them in their respective suitcases for their return flight. Unfortunately, the airline manages to lose both suitcases. Because the airline doesn't know the value of the lost souvenirs, it asks each traveler to report independently a value. The airline agrees to pay each traveler an amount equal to the minimum of the two reports. If one report is higher than the other, the airline takes a penalty of $20 away from the traveler with the higher report and gives $20 to the traveler with the lower report. If the reports are equal to one another, there is no reward or penalty. Neither traveler remembers exactly how much the souvenir cost, so that value is irrelevant; each traveler simply reports the value that her type determines she should report. There are two types of travelers. The High type always reports $100, and the Low type always reports $50. Let h represent the proportion of High types in the population. a) Draw the payoff table for the game played between two travelers selected at random from the population. b) Calculate the fitness function for both types. c) Describe all the equilibria of this game. For each equilibrium, state whether it is monomorphic or polymorphic and whether it is stable. Two travelers buy identical handcrafted souvenirs and pack them in their respective suitcases for their return flight. Unfortunately, the airline manages to lose both suitcases. Because the airline doesn't know the value of the lost souvenirs, it asks each traveler to report independently a value. The airline agrees to pay each traveler an amount equal to the minimum of the two reports. If one report is higher than the other, the airline takes a penalty of $20 away from the traveler with the higher report and gives $20 to the traveler with the lower report. If the reports are equal to one another, there is no reward or penalty. Neither traveler remembers exactly how much the souvenir cost, so that value is irrelevant; each traveler simply reports the value that her type determines she should report. There are two types of travelers. The High type always reports $100, and the Low type always reports $50. Let h represent the proportion of High types in the population. a) Draw the payoff table for the game played between two travelers selected at random from the population. b) Calculate the fitness function for both types. c) Describe all the equilibria of this game. For each equilibrium, state whether it is monomorphic or polymorphic and whether it is stable.

Answer rating: 100% (QA)

a Low type High type Low type 50 50 100 100 High type 100 20 50 20 The expected payoff to the Low ty... View the full answer