Epic Systems Interview Question
YES ! =8-) Always bid minimum: $1. Here's why
Let V=value-to-seller and B=buyer's bid
If V > B then there is NO SALE because the seller would lose money.
The universe of solutions has upper bound = B and lower bound = 1
Profit for buyer P = 1.5*V - B
Since probability density is uniform, the expected value of buyer's profit P is simply the average of the max and min values.r
For any bid B, Pmax is when V=B
Pmax = 1.5*B - B = 0.5B
and Pmin is when V=1
Pmin = 1.5 - B
the average these is the expected value of bid B,
P(B) = (0.5B +1.5- B)/2 = 0.75 - 0.25B
So 100 is the worst bid with a loss of (24.25)
Only three bids do not lose money. 1 wit EV 50 cents, 2 with EV 25 cents, 3 with EV zero, breakeven. ONE IS BEST
Without answering, here is a clearer explanation of the puzzle. Pretend you bid 40 on the oil well. The actual value has an equal chance of being any number from 1-100.
Case 1: The oil well is worth 57. The owner decides not to sell it to you because that would be selling at a loss
Case 2: The oil well is worth 30. The owner sells it to you making a profit of 10. The well is worth 45 to you (1.5*original). You make a profit of 5.
Case 3: The oil well is worth 15. The owner sells it to you. You can't back out. You've overpaid by $25 dollars.
Clearly bidding $40 is a losing proposition. If you bid $40 and the well is...
above $40: no sale
between 27-40: you make a profit
between 1-26: you lose money
This logic carries as you keep decreasing the number. The probability that you lose money is higher than the probability that you make money.
Then we have "Only three bids do not lose money. 1 wit EV 50 cents, 2 with EV 25 cents, 3 with EV zero, breakeven. ONE IS BEST" from Anonymous
This seems right, except when I do it in my head I come up with Expected Value from bidding $2 as also being 50 cents, but it's late at night and I could be missing something.
expectation for them: 51;
expectation for you:76,5.
make a bid between these two...
(is there a unique answer to this question?)
You need to give as much as possible of the feasible amount so that they don't bail out of the agreement. So you need to offer 76.
I think answer is $75.50. Here is how?
to buy 100 oil well = summation(1+...+100)= $5050
with 1/2 chance of success in each well, 50 of 100 will succeed. Each giving profit of $50.
total profit = 25*$50 = $2500
profit + cost = $7550, so we can bid $75.50 to each well and make sure we do not end up in loss.
Always bid minimum??? 1$ :))
- Nix September 22, 2009