## Solution for Managerial Economics 4th Edition Chapter 18, Problem 1

by Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
147 Solutions 23 Chapters 104008 Studied ISBN: 9781305259331 5 (1)

# Chapter 18, Problem 1 : 18-1 Effects of Collusion You hold...

## 18-1 Effects of Collusion

You hold an auction among three bidders. You estimate that each bidder has a value of either \$16 or \$20 for the item, and you attach probabilities to each value of 50%. What is the expected price? If two of the three bidders collude, what is the price?

## 18-1 There are eight possible value combinations for the three bidders, and each is equally likely. These are given in the first three columns of the table below. The fourth column (equal to the second highest value) is the resulting auction price without collusion. The expected price is (4/8)\$16+(4/8)\$20=\$18.

Imagine that bidders 1 and 2 collude. They would be willing to bid up to the maximum of either of their values, but will not bid against each other. Effectively, the auctioneer faces two bidders represented in the right three columns of the table below. The only time the collusion impacts price is when the two colluding bidders have the two highest values (\$20 and \$20) and both are higher than the next highest value (\$16). In this case, by not competing against each other, they drive the price down from \$20 to \$16. The expected price is (5/8)\$16+(3/8)\$20=\$17.50

 Bidder 1 Bidder 2 Bidder 3 Price Maximum of 1 and 2 Bidder 3 Value Collusion Price \$16 \$16 \$16 \$16 \$16 \$16 \$16 \$16 \$16 \$20 \$16 \$16 \$20 \$16 \$16 \$20 \$16 \$16 \$20 \$16 \$16 \$16 \$20 \$20 \$20 \$20 \$20 \$20 \$20 \$16 \$16 \$16 \$20 \$16 \$16 \$20 \$16 \$20 \$20 \$20 \$20 \$20 \$20 \$20 \$16 \$20 \$20 \$16 \$16 \$20 \$20 \$20 \$20 \$20 \$20 \$20