I firmly believe that when a parent brings their child to a shared play area or play group, then they confer to the rest of the attending guardians the right to interact with that child. (I also believe that each attending guardian has a shared responsibility to ensure the safety of the children and the surrounding property.)
In this case, if another child is just taking toys from your child, I believe it is within your rights to address the other child. I would calmly retrieve the toy, and say something to the effect of, "I'm sorry, my son was playing with that, so I need to take it back. But, if you ask him to share I'm sure he'll let you play with it." I usually make it a little more personal by adding my son's name. If I don't know the child I'd ask for theirs, too.
Obviously, with your son only being a year old, he may not get what's going on anyway, and the other child is really just asking you for permission (which is fine). The older child, however, does understand. You're teaching him, at the very least, that your child isn't easy pickings, and at best you're reinforcing his parent's lessons about sharing.
I don't think it's necessary to have to go directly to the parent of the other child, unless they are doing something that's actually harmful to your child and they need to be physically removed. If the other adult happens to be uncomfortable with you speaking directly to their child, but you were being courteous, respectful, and calm, then the fault is with the other adult. If they don't want to be around other adults who take the supervision of other children seriously, then they're free to not attend the communal activities.
In my personal experience (I have a 20 month old), this technique works for both myself and my wife. Our apartment complex has a shared playground, and one or both of us are often out there supervising. Some of the other younger children don't have very good sharing skills, so we often have to address them and ask for toys back.
However, are general preparation for this activities follows this plan:
- Bring toys with the intent of sharing some of them.
- If another child would like to play with a toy our son is actively using, we ask our son if he wants to play with another toy instead.
- If we want to encourage sharing and playing together, we'll get down with our son and invite the other child to play with us (and offer that child one of the free toys).
- If we don't want to lose track of all of our toys, we will tell the other children that they can play with them but they have to stay in [this] area.
- I do not allow any children to take our toys onto playground equipment, and will take/ask for them back if they do. (There's too much liability.)
- If our son is adamant about not sharing a particular toy at that moment, we usually try to capture his attention with a different activity or different toy. This is fairly easy at his age, and prevents focusing on the negative behavior.
- Sometimes we just have to say, "No." But usually, it's more like "I'm sorry, he just started/is really interested in playing with that. When he's done, he'd be happy to share."
When our son gets older, I know we'll have to resort to other techniques. That's an answer for another question, anyway.