Three astronauts are determining what items to bring and share on a mission to Mars. Weight is a big factor on such a mission, so each astronaut is given a fixed allocation for any items she wants to bring. For items to be shared among all three, they have decided to deduct the weight equally from each of their weight allocations. One particular item they are considering sharing is a DVD player, which weighs 3 pounds. In terms of weight, astronaut A places a value for the DVD player of 1.5 pounds, astronaut B a value of 1.25 pounds, and astronaut C a value of 0. The net benefit is the value they place minus the weight they have to deduct.

(a)Would a majority vote result in bringing the DVD player to Mars? Is this outcome efficient?

(b)Show that the Clarke tax induces truth-telling as a dominant strategy if each individual reports independently his own net benefit [Note that in this case the Clarke tax is an amount of weight the astronaut has to forego from her allocation that is not redistributed to the other astronauts]

(c)Compare the results in parts (a) and (b) and interpret the difference, if any.