Can I negotiate to have one month or more of free rent?

My cousins and I were planning to live together in New York since we all work there. Since they are busy with their work, I suggested finding a place for us. I found a three-bedroom apartment in Brooklyn. The place is nice with a lot of space. I am applying for a one-year lease apartment that I will share with my cousins. I would like to pay one-year rent upfront for my share of the apartment not for the entire apartment. I know it sounds being selfish. Nevertheless, they earn a lot more than me and I want to save money. Is there an incentive for one tenant on a lease to pay one year's rent in advance? Would I be able to use this tactic to lower the rent? Can I negotiate to have one month or more of free rent?