Consider a standard position auction. There are three positions: Top (T), Middle (M) and Bottom (B). Position T receives xT = 150 clicks per day, position M receives xM = 100 and position B receives xB = 50 clicks per day. There are five bidders (B1-B5) with the following dollar values per click: v1 = 12, v2 = 10, v3 = 7, v4 = 5, v5 = 3.

(a) Verify whether bidding your value will be an equilibrium of the GSP auction (Google).

(b) Find an equilibrium of the GSP auction (Google) with the maximum revenue.

(c) Find an equilibrium of the GSP auction (Google) with the minimum revenue.

(d) Find the equilibrium of the Vickrey auction (Facebook). Calculate auction revenue.