I'm unsure if the police can even technically fulfill this request, especially if the trespassers are playing a game with you. It takes time for the police to show up, and it's not a crime to be on a sidewalk. It takes one second to step from your lawn to the public sidewalk. The police may have no obvious reason to arrest these individuals. Also if you join "the game" with the gang, the gang has more skills and more interest in that game than you do.
Ultimately a "one man vs. a hundred" situation has no good solution. You may have two gang members arrested, and next week receive a Molotov cocktail in the window when you are at work - a gift from the rest of the gang. They'd love that. If you think it's surrender, it's not - it's simply the fact that your army is much smaller than the other army. Per Sun Tsu, you should avoid fight in such a situation because you can't win. And that's why gangs proliferate - because they are better armies than the police and the citizens (considering laws of self-defense etc.)
Another concern is that the police don't take ultimatums. They don't care how many times you are bothered - one or a thousand. If you attack someone outside your house it doesn't matter to them how often you were baited before. Maybe the judge will take that into account, but the police deals with cold facts.
Actually, it seems the more often you have to call the police, the less often the police respond. At least, that has been my experience/observation, after living in several different neighborhoods.