I guess it would benefit all the buyers if they don't push up the price too much then again if the price is seen as low / in a way there one would had wanted more I guess one may want to pay more (then again it's ok getting less stock which you think you can do say 20% return on than twice as many but which you can only do 10% on
Then again at least when it comes to purchasing lots of stocks many institutions are ok with paying a premium over the regular price to get what they want and hence paying "too much" relative the regular market price.
I don't know whatever the price normally end up being lower or higher than what the stocks will trade for later on.
I also think it differ how it's done. I don't know for sure but it may be the case that here (Sweden) it may be more common to give rights to purchase the new stocks for the old stock holders whereas say in the US it may be more common to look for institutional purchasers of them.
Both methods exist at least. There's also the possibility of just offering shares for a fixed price and then people can sign themselves up for interest and then have a lottery or give them the stocks they could get out from the ones one wanted to create.