An arbitrator will decide in the next two weeks whether to grant so-called Bird rights to Jeremy Lin and three other N.B.A. players in a case that could have a profound effect on the Knicks’ roster.

Lawyers for the N.B.A. and the players union spent more than three and a half hours on Wednesday presenting their arguments to the arbitrator, Kenneth Dam, a professor at the University of Chicago law school.

The union contends that a player claimed on waivers should retain his Bird rights, which allow a team to re-sign a player without respect to the salary cap. The league contends that Bird rights are lost once a player is waived.

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