Finding ways to bid for items, which has a normal distributed price This is an interview questions, I am not quite sure how to solve. The question is stated as this:
Suppose that you want to buy a specific type of car, but you don't know anything about cars (you can't find the underlying quality or the real value). But dealers know about cars and they know exactly how much a car is worth (real value). 
Now you are given a list of prices that different dealers bought at, but the list doesn't show which dealer bought which car. The price is normal distributed. Assume there are infinite number of dealers and the price dealers bought at is considered as the true value of the car.
If you can only bid once for each dealer, and that dealer either accept or decline your offer. Dealer will only accept your offer if and only if your offer is above their buying price.
The question is, how to bid or what price to bid, so that you minimize the loss (the price you offer minus the real value). Assume that you only need to buy one car so you can bid as many times as you want until your offer get accepted.
(Interviewer mentioned mean and standard deviation, but I still couldn't figure out.)
 A: This is my guess...
The loss function: The price you offer minus the real value  $P-R$ ,  ($R\sim N(\mu,\sigma^2)$)  may be related to a risk function. In econometrics and statistics this  is rather standard: http://en.wikipedia.org/wiki/Risk_function
Something I'm assuming is that you are interested in minimizing the (expected) deviation with respect to the real value i.e. minimizing the losses yes but also the gains. This implies minimizing the positive expected difference: 
$R(P,V)= E(P-R)^2$ (The mean squared error http://en.wikipedia.org/wiki/Mean_squared_error)
It can be shown that this is equivalent to 
$R(P,V)= \sigma^2 + (P-\mu)^2$ 
where we don't have control over the first term (the variance) so to minimize $R(P,V)$ P should be as close as posible to $\mu$, this implies bidding P=mean(prices in the list).
But still I'm not sure as he states that the real value is normally distributed !Moreover, we can consider R to be fixed and P to be our estimator... I guess the answer would be the same for a different reason
