Every day the Repo finance company holds a sealed-bid, second-price auction in which it sells a repossessed automobile. There are only three bidders who bid on these cars, Arnie, Barney, and Carny. Each of these bidders is a used-car dealer whose willingness to pay for another used carfluctuatesrandomlyfromdaytodayinresponse tothe variation in demand at his car lot. The value of one of these used cars to any dealer, on any given day is a random variable which takes a high value $H with probability 1/2 and a low value $L with probability1/2.The value thateachdealerplacesonacarona given day is independent of the values placed by the other dealers. Each day the used-car dealerssubmitwrittenbidsfortheusedcarbeingauctioned.The Repo finance company will sell the car to the dealer with the highest bid at the price bid by the second-highest bidder. If there is a tie for the highest bid, then the second-highest bid is equal to the highest bid and so that day's car will be sold to a randomly selected top bidder at the price bid by all top bidders.

d)If there is no collusion and every dealer bids his actual valuation for every used car, what is the probability on any given day that Arnie gets a car for a lower price than the value he places on it? (Hint: This will happen only if the car is worth $H to Arnie and$L totheotherdealers.)Supposethatwemeasurea cardealer's profitbythe difference between what a car is worth to him and what he pays for it. On a randomly selected day, what is Arnie's expected profit?