In this question, you are asked to investigate the effect of collusion in the se

Question

In this question, you are asked to investigate the effect of collusion in the second price sealed bid auction. Throughout, you may assume that the bidders’ are drawn independently from a uniform distribution on [0, 1] and that bids outside the interval [0, 1] are inadmissible.

Assume that impediments to collusion are minimal, in the following sense. All bidders involved in a bidding ring can costlessly determine each other’s valuations. Furthermore, the ring has no problem making (and enforcing) agreements on side any payments necessary to guarantee voluntary participation of all ring members. Thus the objective of the ring is to maximize the joint surplus of its members.

(a) Consider first the case of two bidders. If they form a ring, what two bids should they optimally submit? Explain your answer.

(b) Suppose now that this ring faces an enforcement problem because ring members cannot be prevented from breaching the agreement. If the ring has to guard against this possibility, will it require different bids from its members?

(c) Suppose instead that there is a third bidder, who does not participate in the ring. Does the presence of this extra bidder change the bidding behavior of the ring members?

Explanation / Answer

A. In the case of two bidders colluding, they should start with the lowest possible bid. For example. If one person bid 1 dollar on one item and won then the next item the other bidder won with a staarting bid of 2 dollars, since the bidders collude they will share the cost of (1+2)=3/2=1.50 each. This is the mindset two colluding bidders have. B. In this case, another bid would be required. However, the bidders will still bid the two lowest price. For instance, the first item starting at 1 dollar increasing in 1 dollar increments will end at 2 dollars and the second item starting at 2 dollars will end at 3 dollars. This two bidder will again split the pre arranged cost of (2+3)=5/2=2.50 each C. In the case a third bidder enters the picture one of the members will not bid because it will drive the price up. The price of the bid in this case may chance depending on the preference of the the new bidder. Since he or she will not be colluding, it is wise for the colluding team to let the other bidder bid first and be aa second bidder ready to outbid the new bidder.

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