you currently lack the funds to pay each of the others their

you currently lack the funds to pay each of the others their probable fair share. You will not receive the collection, but wish to receive as much money as possible. You have no knowledge of the amounts in each of the sealed bids, but strongly suspect that Abraham will bid between $10,000.00 and $12,000.00.

Given that you cannot afford to “win” the process, describe how you will go about deciding what to put down for your own estimate of the value of the collection.

Solution

Solution :

Since there are now four bids, your fair share of the collection will be one quarter of your bid. Since there are no other items involved, you will be paid that same amount as long as you do not win the bid, plus one quarter of any amount remaining in the pot after each of the losing individuals are paid.

Since you suspect that Abraham will bid between $10,000 and $12,000, his fair share can then be expected to be between $2,500 and $3,000. Without any information about the other bidders, this represents an approximate minimum risk of payment should you win the bid. Your actual risk would be higher, assuming that the others submit bids that are significantly greater than 0.

You will maximize your payment by bidding as close as possible to Abraham\'s bid, without exceeding it. This will give you a full quarter of your losing bid, plus one-quarter of any amount remaining in the pot after the other players are paid.