Fair share math

The Center City Anuraphilic (frog lovers) society has fallen on hard times. Abraham, Bobby and Charlene are the only remaining members and each feels equally entitled to take possession of the society’s collection of live rare tropical frogs. The decision is made to use the method of sealed bids and fair shares to decide who will take possession of the entire collection and how much will be paid in compensation to the other members.

Abraham unseals his estimate of the value of the collection at $12,000.00. Bobby’s estimate of the value of the collection is $6,000.00. Charlene values the collection at $9,000.00.

Who receives the collection of frogs?
What is each person’s fair share of the monetary value of the collection?
Why is the monetary amount of each fair share different?
How much money is owed to each of the two people who do not “win” the collection of frogs?
In your opinion how “Fair” is the process described above?
Now pretending for a moment that you like frogs, we will insert you into the situation under special circumstances. Despite (or perhaps because of) your love of all things amphibious, 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.
Comment on your peers' responses, addressing the following:

Do your peers' responses address all of the points of the assignment?
Are the answers and the reasoning behind those answers clear?