A company wants to buy commodity materials (paper for the company) for the month of February through an auction. Traditionally such auctions take on the following format: Bidders subsequently submit ever lower prices until nobody bids. The buyer then assigns the monthly contract to the supplier who submitted the lowest price (see below for a visualization).

In this case, the company does not want to use this format. Instead, it will ask the suppliers to submit only 1 (sealed) bid and then assign the entire contract to the lowest bidder. However, that bidder does not get the monthly contract at the price (s)he submitted but at a higher price namely the price submitted by the second lowest bidder.

You are one of the 10 bidders (paper companies) that will bid in this auction.

Your objective is to maximize Excess Value which is the difference between the revenues you obtain in the auction (if you are the lowest bidder) and your ‘walk-away value’, which is essentially your total opportunity cost of producing the paper. Hence it is better NOT to get the contract (and making zero excess value) than getting the contract at a price that is less than your walk-away value (the objective is not to ‘win’ but to maximize excess value)

You know the number of other bidders (10, including you) and have imperfect information about their walk-away value just like they have imperfect information about your walk-away value. You do know that their walk-away values range somewhere between $500 and $1000 and that each valuation within this range is equally likely. Your walk-away value is only known to you and is also between $500 and $1000.

Question 1: If the buyer only buys paper for the month of February and your walk-away value is K (a figure that I will communicate privately to your team), what bid do you submit (the actual figure)? Explain why.

Question 2: Assume that this auction is organized for the monthly contract for February and that the buyer will also buy paper in the remaining months of the year (not necessarily through an auction), what is a possible benefit that the buyer obtains of using this one-shot auction format instead of the traditional auction format, depicted above?).

 

Amount BIDDING EVENT (Product Type A) 0.59 0.55 0.51 0.47 0.43 0.39 0.35 0.31 0.27 lowest bid at $ 0,19 0.23 0.19 10:00 10:05 10:10 10:15 10:20 10:25 10:30 10:35 10:40 10:45 10:50 10:55 11:00 Time End of Supplier 1 Supplier 2 Supplier 3