Can a parent negotiate with their children?

All the time. My authoritarian mother in law was watching our kids for a few days while we were away. Afterwards, she told us of an issue she had had with them and said, “Since I know you (my husband and I) are so found of making deals with them, I made a deal with them.” I don’t think she really approved of the way we managed but she was willing to try it.

Sure, as a drill Sargent would negotiate with raw recruits. ;)

Isn’t that what parenting is, pretty much. Unless your style of parenting is that of an authoritarian tyrant.

Of course, but it gets expensive.
Can you sell kids on ebay yet?

Even with an authoritarian parent, it’s just a different type of negotiation. The more tyrannical the parents, the more the children react, intentionally or not, in some fashion, sooner or later…

Sometimes, sometimes not. “because I said so” is a phrase frequently used by parents.

Every night, my mother would ask, “Pied, will you set the table?”

One day, I responded, “What if I said, ‘No’?” Mom said, “Oh, you don’t have a choice; I was just making it sound pleasant.” And then she laughed.

Every situation is unique. Sometimes making a deal is called for.

Having said that, if they had chores (which they did) they did them. No bargaining.

I had a bedtime routine for them, again no bargaining.

I would never do anything to get them to try a new food beyond offering it to them.

It depends on the age. Teaching them how to value their time is an important life lesson, as is taking responsibility to hold up their end of an agreement. But it is also up to the parents to hold them to that responsibility and not give in to try being nice.