A seller will run a second$-$price, sealed$-$bid auction for an object. There are two bidders, a and b$,$ who have independent, private values vi which are either $0$ or $1.$ For both bidders the probabilities of vi $=0$ and vi $=1$ are each $1/2.$ Both bidders understand the auction, but bidder b sometimes makes a mistake about his value for the object. Half of the time his value is $1$ and he is aware that it is $1$; the other half of the time his value is $0$ but occasionally he mistakenly believes that his value is $1.$ Lets suppose thatwhenbsvalueis$0$heactsasifitis$1$withprobability $21$ andasifitis$0$with probability $12.$ So in effect bidder b sees value $0$ with probability $14$ and value $1$ with probability $34.$ Bidder a never makes mistakes about his value for the object, but he is aware of the mistakes that bidder b makes. Both bidders bid optimally given their perceptions of the value of the object. Assume that if there is a tie at a bid of x for the highest bid the winner is selected at random from among the highest bidders and the price is x$\mathrm{.}270$ CHAPTER $9.$ AUCTIONS $($a$)$ Is bidding his true value still a dominant strategy for bidder a$?$ Explain briefly$($b$)$ What is the sellers expected revenue? Explain briefly