# Not sure how to use this formula for auctions

In my textbook I was given this formula for auctions:

As far as I understand, $N$ is number of people who place bets, $P_{personal}$ means my subjective value of the current lot (it's also assumed that it's the highest subjective value among people placing their bets), $P_{max1}$ is maximum price (not sure what it means).

My textbook seems to imply, that in order to avoid "Winner's curse" our bet must be equal to $P_{max2}$ because it reflects the true value of a traded lot. Otherwise, after such victories we will go broke.

In order to calculate $P_{max2}$ we use following formula:

My difficulties are with formula for $P_{max1}$.

1.For what kinds of auctions can I use this formula?

2.What is the difference between $P_{personal}$ and $P_{max1}$?

3.Why is $P_{max2}$ supposed to be the real value of the traded lot?

4.What to do if I'm not sure that my subjective value of this lot is the highest among participants?

5.Let's suppose that I want to win the lot in order to resell it for higher price. On one hand, if I don't place high enough bet, then it will mean that I will win less frequently. And it can be painful because I can have fixed costs to be paid, no matter if I win or lose. On the other hand, by increasing my bet I decrease my profit margin. So it's unclear for me how to calculate my $P_{personal}$ in this case.

6.Please, give me the name of this formula, if it has name.

• Since this is related to the winner's curse, the auction is probably a form of common value auction. However, the information you provide does not seem sufficient to answer your questions. Try to re-read your textbook more carefully. It must have information about the context of the auction, its rules, etc. If not, you should look for a different text. – Herr K. Feb 28 '18 at 20:57
• " If not, you should look for a different text.". Can you recommend any sources where I can find the same formula? – user161005 Feb 28 '18 at 22:28
• What's your level of study? – Herr K. Feb 28 '18 at 22:30
• @herr-k Undergraduate – user161005 Mar 1 '18 at 6:12
• Consider the optional readings suggested in Phil Reny's undergraduate auction theory course. – Herr K. Mar 1 '18 at 17:37