Auction Theory, 2nd Edition

166 Bidding Rings

We saw in Chapter 2 that without a cartel the optimal reserve price was

r

∗

=

1

2

.

Now suppose that both bidders are members of a cartel and suppose that

the seller sets a reserve price of r. The cartel would bid max

{

X

1

,X

2

}

and would

purchase the good for r if this bid exceeds r. The seller’s expected profit is

r ×Prob

[

max

{

X

1

,X

2

}

> r

]

=r



1−r

2



which is maximized by setting r

∗∗

=

1

√

3

>

1

2

=r

∗

. 

11.2 COLLUSION IN FIRST-PRICE AUCTIONS

The operation of bidding rings in first-price auctions introduces some new ele-

ments. First, unlike in a second-price auction, the cartel agreement in a first-price

auction is not self-enforcing and, hence, is somewhat ...