Mixed Strategies: Consider a seller who offers a single private value good using a first-price sealed-bid auction. There are two potential buyers, each with a valuation that can take on one of two values, 0; € (4, 8), each value occurring with an equal probability of [. The players' values are independently drawn. Call the type with 0, = 4 the "low" typland 0; = 8 the "high"type.a.Show that in a Bayesian Nash equilibrium the low must be using apure strategy bid b, = 4. (Hint: First show that in a Bayesian Nashequilibrium the low type cannot be using a pure strategy bid b, < 4.Next show that in a Bayesian Nash equilibrium the low type cannot be using a mixed strategy with two different bids.)b.Show that given the fact described in (a), in any Bayesian Nash equilibrium the high type will never choose a bid by > 6.c.Show that the low type choosing b, = 4 and the high type choosingby uniformly from the interval (4, 6] together constitute a Bayesian Nash equilibrium.d. Calculate the expected revenue to the seller given the Bayesian Nash equilibrium in (c). How does it compare to the expected revenue he would obtain from an English auction?