The cost of an engagement party should be shared among the bride and groom. It can also be on the partner who wants to make it as a surprise. However, "who pays for what" is supposed to come in during the wedding arrangements.
The person who wants to throw the engagement party usually pays for it. That's presuming you're talking about a party *after* the proposal so you can celebrate getting engaged. If you want to get really traditional, the bride's family pays for everything up to and including the marriage.
it depends usually the brides never pay !!! so if she is gonna pay you mean her dad it usually is the husband and the groom's father who pays but if you plan it all you will have to pay it all but if you both plan it of course you will have to let go of some items but you wont have to pay all depends on what you do
Traditionally? Very sorry, no passing out tabs for food and such, unless someone agrees to help pay beforehand. For an engagement party, the hosts foot the bill. It's not assigning costs like the wedding and rehearsal dinner, it's just whomever wants to help chips in and you go with that budget.
There can be multiple parties of course, depending upon family size or just plain preference. The bride's family generally hosts the first one in that case (parental group effort possible). When the couple are established adults the parents might not have one at all. If there's just one party, it's generally either the couple planning (and paying), or friends. If someone offers to pay for the food, specifically, or the hall, fantastic. Let them.