The rules at Hillside are vague when it comes to the etiquette of toys – "Exercise caution with food and toys in the Park" – but the rules among the dogs are so idiosyncratic that we humans have to regulate how sharing works on a highly ad hoc basis.
Here's how I deal with Daisy, Pickering, Hermia: I take three or four balls, most of them the orange and blue Chuck-it balls that get a good bounce, and one squeaky ball for emergencies. Daisy is insane about fetch. Pickering learned the second half of fetch (bring the ball back) from Daisy, but would really rather get some rough play that turns into a game of catch-me. Hermia likes to trot or lie around clutching a ball in her mouth. She's interested in chase and battle, but will carry the ball into the fray, somehow barking around it.
This is the basic canine personality template from which I work. There are, however, a number of kinks along the way.
Daisy is the loudest and safest dog in Hillside Park. The only thing she wants is to fetch her ball and occasionally collapse and monopolize a watering spot. It doesn't matter which ball she gets on the first toss, but after that she is exquisitely sensitive about whether it's hers or not. She will follow a dog that takes her ball, barking, but she will never fight for it or go in too close to grab it when the dog has dropped it. Daisy comes from solid hunting stock and I'm convinced that she is transported to a Montana watershed where she would never tear the duck by competing with another retriever. Interestingly, she will pee on her way out of the park but has never taken a dump in it. The dog run is her holy, ancient ground.
Hermia is a thief if she likes some other ball better and she's incredibly stubborn. I have a 50/50 chance of getting a ball back from her. Squeaky ball usage #1.
daisy hermia If the owner says something like, "It's your fault for bringing balls in the park." I go after the ball myself, firmly but soothingly. Squeaky ball usage #3.
Recently, I had a situation I couldn't read. An owner threw out a Wubba (a sort of octopus-shaped toy made from fire hose material) for his dog, who carried it around for a minute and then dropped it. Pickering eventually got around to finding the Wubba and another dog started tug-of-war over it. They had some fun and then Pickering went back to chewing sticks or chasing his ball, and the other dog chewed the Wubba pretty much to threads. On the way out of the park, the owner made a noise that might have been in my direction and might have been a reprimand, possibly about the Wubba.
I honest-to-St. Rocco don't know what the owner (who I call "Mother Superior") or my responsibilities in this scenario were. If my dog had ignored its Wubba, I'd have packed it up. If a dog took it, I'd either ask for help or, less preferably, get it back myself. Finally, Pickering lost interest in it and it was a dog unknown to me who killed it. Mother Superior did nothing about the Wubba until that noise seemed to drift across my radar as we climbed the hill to the gate.
I've had run-ins over toys before, when my dogs thieve or are thieved from, and I have plans of action. Mother S. seemed to have no such thing but I remain bothered by the feeling that I should replace the Wubba.
At which point, Pickering or some other dog will pick it up and the whole thing will start again.