This happens similarly in American professional sports. Young, incoming players can't choose their own team - instead, they're subject to a draft, and controlled by the team that drafted them for anywhere from 4 to 10 years. During that time, the players make very below market money and have no leverage. Then, after they become a free agent, they get overpaid relative to equilibrium. The veterans that have more say in the union consistently bargain more benefits and agree to hose the young incoming players in return.
Sports labor markets seem pretty screwed up overall, partly because it's a very strange market. Are teams in competition with each other? Or is the league one entity, in competition with other leagues and even other sports?
Some other sports-employment models, broken in different ways:
1. The owner-collusion model. A league is exempted from anti-trust laws, and the owners get together to institute rules. There's a draft, and new players can't be hired except via the draft. There is no free agency, or limited, owner-supervised free agency. Basically the "market" is you either do whatever the system tells you, or you leave the league entirely. Most new sports leagues being set up follow this model (e.g. Major League Soccer).
2. The contracts-ban-free-agency model. There's no draft, and you can sign with any team you want. However, the owners have officially or unofficially standardized on an employment contract that requires you to get your team's permission before signing on with any other team, even after your contract expires. Basically a noncompete clause. This is more or less how European club football worked prior to the EU's Bosman ruling invalidating that variety of noncompete (among other things).
The NFL is (currently) the exact opposite of what you describe. Draftees entering the league right now earn disproportionately higher amounts than many veterans, and it is a major point of contention in the upcoming CBA bargaining.
