Playing Detective Consider a standard position auction. There are...

Playing Detective

Consider a standard position auction. There are two positions: Top (T) and Bottom (B). Position T receives xT = 200 clicks per day and position B receives xB = 100 clicks per day. There are three bidders (B1 - B3) with the dollar values per click that satisfy v1 > v2 > v3 > 0. All values are positive integers. In this question you will recover values v1, v2, v3 step-by-step by following the list of clues.

The list of clues (proceed in the given order)

(a) Write down restrictions on values that are consistent with the fact that b1 = 20, b2 = 7, b3 = 4 is an equilibrium of the GSP auction.

(b) Write down further restrictions on values that are consistent with the fact that b1 = 10, b2 = 3, b3 = 2 is NOT an equilibrium of the GSP auction due to Bidder 3 having a profitable deviation (strictly positive). At the same time, Bidder 1 and Bidder 2 do not have profitable deviations.

(c) Write down further restrictions on values that are consistent with the fact that p1 = 8 and p2 = 6 are the highest "per click" market clearing prices.

(d) Write down further restrictions on values that are consistent with the fact that Vickrey auction generates 1400 in revenue.