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) Graph the fitness of the High type, with h on the
horizontal axis. On the same figure, graph the fitness of the Low type.
(c) Describe all of the equilibria of this game. For each
equilibrium, state whether it is monomorphic or polymorphic and whether it is