I've been reading through Walter Neale's 1964 classic "The Peculiar Economics of Professonal Sports." In this paper, he describes various oddities about pro team sports as compared to the economic theory an economics student might learn, particularly those from the early 60's.
Neale argues that the product in the sports industry is competitions. If the product is competition, then a team is an input in the production process and not "the firm" as understood in economic theory. Instead, a league, like the NFL, is the firm in this case. He argues that the market for competition within a particular sport is a natural monopoly.
I think he is correct. Within a team sport played at a particular level, there can only be one "best team". The history of the past 150 years, at least here in the states, is a tendency towards one league. Leagues have started, some folded, some became dominant. Rivals have formed. Some have folded, some have merged with the dominant league, while others have partially merged with the dominant league while the remaining teams folded.
The NFL goes back to the 1920's. Over the years there have been various rival leagues that have popped up: the All American Football Conference in the 1949's; the American Football League in the 1960's, and the United States Football league in the 1980's, just to name three.
The AAFC partially merged with the NFL; the rest of the league folded. The AFL fully merged with the NFL, giving us the NFL we know to this day. The USFL league folded although some of its players, such as the Buffalo Bills former quarterback Jim Kelly, starred on NFL teams.
These days we are seeing such mergers within college sports, aka "conference realignment."
At the end of the paper, Neale gives some cautionary advice to those who make, practice, and adjudicate antitrust law as it pertains to professional team sports. He concludes:
... professional leagues have every economic ground to appeal to legislatures, to courts, and to the public that (w)e fall if you divide us; (w)e stand if Johnny Unitas.
Analysis: true. Some level of cooperation is required for competition between teams to be commercially viable. Rules must be developed and enforced. A championship format must be formed. Playing schedules must be set, and there needs to be some internal system to deal with the inevitable disputes that will occur between teams.
In other words, when it comes to making competition happen and to make it commercially viable, some cooperation between teams off the field of play is necessary to make the games happen, and in this particular sense leagues are single entities.