Have you considered airsoft or reballing? I used to play airsoft, never played paintball. The land/playing area would usually be provided by someone one of the players knew, private forests, empty barns, junk lots, etc. We all had our own guns. We usually managed to scrape together 5-10 people for our games. Not sure about 100. That sounds rather ambitious for a game(?)
The general trick to owning expensive equipment is to find something with very little depreciation (usually top quality items) and buy used. This makes the carrying cost rather low. For example, my hand planes for woodworking are $300+ each, but I could sell them again for 90%+ of what I paid for them, so my effective cost is only thirty bucks. A brief search on the net reveals one can get 2000 paintballs for $30. Now I don't know if they're any good or not, but that sounds pretty cheap to me. How many shots for a game? 100? That's less than two bucks.
So I think you could do it pretty cheaply if you "invest" the money and do the organizing footwork.
Just to clarify the details of the paintballing example...
Land is a serious problem except once it's no problem at all. If you don't know anyone who has land that they'll let you use, how do you find someone? Everyone I've met that plays paintball cheaply just plays illegally on land that they do not own, which may or may not seem unethical to other people. In my opinion, access to legal land actually is a significant hurdle for many people.
Now, in practice, paint is the main cost. Perfectly good paint costs less than $0.05/ball (maybe $0.03 is a bit low-end), which is usually marked up 100% or more if you're playing on a paid field (this is their main revenue). The problem is, many players are accustomed to a play-style where they burn thousands of rounds ($50+) a day. If everyone agrees to use pump-action guns (cheaper!), you can have nearly the same experience at 1/20 the paint cost. If everyone around you is using semi-auto and burning paint, it's a lot harder to go pump (some people like the asymmetric challenge, but most do not).
Especially living in a city. You also need to travel there (it's almost certainly not accessible by public transport). Paint is the main cost, I do own my on equipment, and most places require field paint. Also, I love walk on paintball with 50-100 people in a giant game. You're going semi-auto and burning a lot of paint, that's part of the game play.
The general trick to owning expensive equipment is to find something with very little depreciation (usually top quality items) and buy used. This makes the carrying cost rather low. For example, my hand planes for woodworking are $300+ each, but I could sell them again for 90%+ of what I paid for them, so my effective cost is only thirty bucks. A brief search on the net reveals one can get 2000 paintballs for $30. Now I don't know if they're any good or not, but that sounds pretty cheap to me. How many shots for a game? 100? That's less than two bucks.
So I think you could do it pretty cheaply if you "invest" the money and do the organizing footwork.