This problem (and the two that follow) concerns collusion among bidders in sealed-bid auctions. Many writers have found evidence that collusive bidding occurs. The common name for a group that practices collusive bidding is a “bidding ring.”* Arnie, Barney, and Carny of the previous problem happened to meet at a church social and got to talking about the high prices they were paying for used cars and the low profits they were making. Carny complained, “About half the time the used cars go for $H, and when that happens, none of us makes any money.” Arnie got a thoughtful look and then whispered, “Why don’t we agree to always bid $L in Repo’s used-car auctions?” Barney said, “I’m not so sure that’s a good idea. If we all bid $L, then we will save some money, but the trouble is, when we all bid the same, we are just as likely to get the car if we have a low value as we are to get it if we have a high value. When we bid what we think its worth, then it always goes to one of the people who value it most.”
(a) If Arnie, Barney, and Carny agree to always bid $L, then on any given day, what is the probability that Barney gets the car for $L when it is actually worth $H to him? ________. What is Barney’s expected profit per day? ________.
(b) Do the three dealers make higher expected profits with this collusive agreement than they would if they did not collude? Explain.
(c) Calculate the expected total profits of all participants in the market (including Repo as well as the three dealers) in the case where the dealers collude. ________. Are these expected total profits larger or smaller than they are when the dealers do not collude? ________.
(d) The cars are said to be allocated efficiently if a car never winds up in the hands of a dealer who values it less than some other dealer values it. With a sealed-bid, second-price auction, if there is no collusion, are the cars allocated efficiently? ________. If the dealers collude as in this problem, are the cars allocated efficiently? ________.