102. Oil Wells
You are an oil mogul considering the purchase of drilling rights to an as yet unexplored tract of land.
The well's expected value to its current owners is uniformly distributed over [$1..$100]. (I.E., A 1% chance it's worth each value b/w $1..$100, inclusive).
Because you have greater economies of scale than the current owners, the well will actually be worth 50% more to you than to them (but they don't know this).
The catch: although you must bid on the well before drilling starts (and hence, before the actual yield of the well is known), the current owner can wait until *after* the well's actual value is ascertained before accepting your bid or not.
You want to maximize your profits. You didn't get rich by scoffing at small dollar amounts. A dollar is a week's wages.
Bids must be in even rounded dollar values. How many dollars should you bid?
Submitted by tartle · Added 7 December 2007
Hint: The seller will only sell to you if you bid either a fair price, or if you bid more than the well is worth to him.
Solution:
Bid $1 for a certain profit of 50 cents, assuming the seller will sell the well at a fair market price. If you bid $2 you may lose 50 cents or you may gain $1, and the average expected profit is only 25 cents. If you bid $3, you might break even, or you might lose $1.50 or you might gain $1.50, so the average expected profit is nothing. All other bids are losing propositions. The classic “winner’s curse” version often assumes values are continuous from $0 to $100. In that version, the right answer is bid $0, because every accepted bid has negative expected value.
Comments (4)
You should bid a cent more than the others....i think XD
I would buy a tenth of the land for 15 bucks (enough to put my wells on and roads or a pipeline to get out), and then get all of the oil on the whole tract through drainage.
Bid at what the current owner think its worth. If you bid more than what they think its worth it will give them ideas....
Your bid must be made before the value is known; but it doesn't have to be accepted until after the value is known.
If your bid is less than the value to the current owner, it will be declined every time. If it is equal to or greater than the owner's expected gain, the bid will be accepted. (if the current owner refuses a bid with value exactly equal, it's impossible for you to make any money at all)
If you bid $1 and your bid is accepted (which it will be 1% of the time), you extract $1.50 worth of oil and net $.50. Expected gain from bidding $1 is $.005.
If you bid $2 and your bid is accepted, you expect to extract 2.25 worth of oil and net .25. Because your bid is accepted 2% of the time, the expected gain from bidding is still $.005.
If you bid $3 and the bid is accepted, you expect to extract $3 worth of oil. (There is an equal chance that the standard amount of oil is $1,$2,$3, and you get 1.5 times that, for an average of $3).
If you bid $4 or more, you expect strict loss.
Alternately, if bids other than a flat amount are allowed, you can bid 100% of the estimated value of oil.
Add a Comment or Suggest an Answer