The Center City Anuraphilic (frog lovers) society has fallen on hard times. Abra
ID: 3123066 • Letter: T
Question
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.
Explanation / Answer
Who receives the collection of frogs?
Abraham receives the collection, as he submitted the highest bid.
What is each person’s fair share of the monetary value of the collection?
Abraham's fair share = $12,000 / 3 = $4,000
Bobby's fair share = $6,000 / 3 = $2,000
Charlene's fair share = $9,000 / 3 = $3,000
Why is the monetary amount of each fair share different?
Each fair share is different because it is based on the individual bids submitted by each person.
How much money is owed to each of the two people who do not “win” the collection of frogs?
The amount that each individual either owes or pays is equal to the difference between their fair share and the value of the item that they won.
Abraham: $4,000 - $12,000 = -$8,000
Abraham pays $8000
Bobby: $2,000 - $0 = $2000
Bobby is owed $2,000
Charlene: $3,000 - $0 = $3000
Charlene is owed $3,000.
This puts $8,000 in the pot. After Bobby and Charlene are paid their owed amounts, there is $8,000 - ($2,000 + $3,000) = $3,000 remaining in the pot.
This remaining amount is divided equally among the three individuals.
Bobby's net payment is then $2000 + $1,000 = $3,000.
Charlene's net payment is $3,000 + $1,000 = $4,000.
In your opinion how “Fair” is the process described above?
It is "fair" in that the rules are the same for all participants. One condition of the process is that each participant does not have any useful information about the other participant's personal value systems. Otherwise, individual bids could be altered so take into account an expectation of how another bidder might value the item, rather than each bid reflecting the bidder's personal valuation of the item. As long as this condition holds true, the process is "fair" in the sense that the risk/reward is evenly distributed across the players.
However, this process will also favor the individual with the deepest pockets, as the highest bidder will always win the item. This means that if an individual wanted an item badly enough, he/she could outbid the others, even though that bid did not accurately reflect his/her true valuation of the item. In a situation involving individuals of disparate resources, this process could be exploited in a manner which would feel "unfair" to the individuals of more limited means.
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.
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.
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