Two companies are interested in buying a plot of land at auction. They have each collected surveys of the value of the land – Company 1 knows s1 and Company 2 knows S2. Neither company knows the value of the other's survey: they only know that it is uniformly distributed on [0,10].
Both companies know that V, the true value of the land, is equal to the average of the two surveys: V = (S₁ + S₂)/2.
a) Company 1 learns that s₁ =7. What is Company 1's current expectation of V?
b) Suppose both Company 1 and Company 2 bid their current expectations of V. Company 1 will only win the auction if s₂ <
c) Suppose Company 1 wins the auction (with both companies bidding as described in part b). What is Company 1's expectation of V conditional on winning the auction?