Dream called about this fight... I told them no. Eddie fights for Bellator.
The meaning of this is up for speculation. Alveraz did just take 3 fights in 3 months, winning the Bellator LW tournament and the $100,000 prize. It is a very real possibility that he simply wants a vacation. However, the wording from Cox implies that Eddie is going to exclusively fight for Bellator, and that Bellator plans to have enough cards to keep him busy, and that they are also willing to match his previous purses.
A matter of concern for both Alveraz and Bellator is the quality of opponents to challenge for his title. With DREAM and the UFC both having contracts of nearly all top 20 LWs, there could be a real problem with contendership.
Edit: In an interview with MMAJunkie, Cox had this to say:
Also, Bellator owns the rights and probably won't allow their champ to fight elsewhere.
Why Cox would have a fighter under multiple contracts sign an exclusive one is anyone's guess, but it probably has something to do with the reason that he let Big Tim fight Ray Mercer two months before his Affliction bout.