This is possible, and you use the iLink feature that all PS2s have (iLink = Firewire, or IEEE1394, under a different name). You can hook together many, many PS2s, provided a) the game supports iLink and b) you have enough connecting equipment! The best way to connect more than 2 PS2s together is via a Firewire hub, which you can buy from any decent PC store, or the Internet, though as I'm not sure where you are geographically I can't really recommend any good online stores. Be careful when buying your Firewire hub though, make sure that the sockets on the hub are the same type as the iLink cables (the squarer 4-pin cables as opposed to the larger 6-pin cables which have that much larger, almost-trapezoid-shaped plug) - but apart from that, it's pretty much a case of plug and go. An example of a Firewire hub to use with PS2s and iLink is this IOGEAR hub - http://playstation-2.cebru.com/videogames/P000IngngjIOOR/6port_Ilink_Battlehub_forplaystation/ - though also note that the picture shows the WRONG type of connectors (those 6 pin ones) - so again, just doublecheck when you buy a hub that it's got the right type ;) otherwise it could be frustrating when you get home.

To add to what he said you can also (only if all ps2's have network adaptors and seperate copies of the game in question) use just a regular HUB and connect them together usung cat5s and select LAN if available.