Artists not signing deals with Ticketmaster lose access to venues, and venues not signing exclusivity deals with Ticketmaster lose access to artists.
There are enough of these on both sides that neither wants to lose the other so they sign.
Side note: I worked at a small ticketing software shop circa the Ticketmaster/LiveNation merger. The CEO got a call from the feds(FTC?) doing background work on the industry's view on how it might affect competition. For the life of me I can't imagine why he said it wouldn't really matter, but I have to assume that Ticketmaster was already so locked in to the industry that perhaps it didn't.