# REU Project: Modeling Information Cost in Auctions

My name is Dan Boylan, and I am a graduate student in the PhD program at the Columbia University Mathematics Department. In the summer of 2002, I participated in the REU (Research Experiences for Undergraduates) program at DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science. DIMACS is located at Rutgers, the State University of New Jersey, not to be confused with Rygar, the Legendary Warrior of 8-bit Nintendo. You can send me email at boylan at math dot columbia dot edu (use symbols where applicable).

I am also a recently graduated math major from Harvey Mudd College in Claremont, California. My other web page is there. But all it has is a maze solving applet I had to make for Principles of Computer Science three years ago.

## My Research

During the REU program, I investigated problems in auction theory under the guidance of Dr. Michael Rothkopf of the Operations Research center here at Rutgers. These models are meant to pay particular attention to the bid preparation process. That is, they will reflect the value of gathering information before the auction: a bidder who invested more effort in researching an item's value before the auction is more likely to submit a bid that is close to the item's actual value.

This value for the item can be broken into two components: a common value v_0 shared by all bidders, and private values v_j, each of which applies to only one of the bidders (bidder B_j). Thus for each bidder B_j, the total value of the item is v_0 + v_j. The common and personal values are each modeled as the sum of a number of independent random variables uniformly distributed on the unit interval [0,1].

Given this model, there are a number of important questions:

• How much money should a bidder spend on evaluating the item?
• Is it better to focus on the common value or the private value?
• Is the item allocated more efficiently if its value is known by everyone?

We would also like to determine how sensitive these answers are to:
• the number of bidders
• the cost and amount of information available
• the type of auction.

More information will follow as I complete the write-up. Here is what I have posted so far.

## Some Papers on Auction Theory

Here is a list of the papers I have used so far as references for this project:

• Klemperer, Paul, "Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Vol. 13, No. 3, pp. 227-286 (1999).
• Milgrom, P.R. and Weber, R.J., "The Value of Information in a Sealed-Bid Auction," Journal of Mathematical Economics, Vol. 10, pp. 105-114 (1982).
• Rothkopf, Michael H. and Harstad, Ronald M., "Modeling Competitive Bidding: A Critical Essay", Management Science, Vol. 40, No. 3, pp. 364-384 (March 1994).