I'm a support associate at a large financial institution who has been asked to do a project for senior leadership. I have done similar work for nearly five years for the company and deliver quality, however, another team of significantly more senior analysts has been asked to do the exact same thing, down to the exact same metrics, within days of be asking me. Over the last year, leadership has done this a number of times and the team they've chosen is generally responsible for this level of work. The problem isn't pay/title (although an additional 20k and title would be nice) but the culture it's creating; who can get this done first and who will be okay with scope creep; One guy versus a team of Sr. Analysts. Any suggestions of how to graciously bow out at this point?
So it really comes down to four options: play by their rules and win at all costs, play by their rules above board, try to modify the rules, or don't play.
Play by their rules and win at all costs - If you can beat this team in terms of delivering a better product then you win and look like a hero. To do this and only this you can ensure that your use of common resources at very least is higher priority than theirs. This would require leveraging your connections. It's cutthroat and doesn't sound like a path you want to take.
Play by their rules and play above board - Discuss use of shared resources with them as well as your manager and their manager and ensure that neither side is getting an unfair leg up. Simply view this as a "selecting multiple internal bids" situation and do your best to do right by the organization. The risk here is that if the other side is playing cutthroat you are putting yourself at severe disadvantage.
Change the rules - Unless specifically forbidden from doing so just start working with the other team, when called on it say that since both sides had been given the exact same assignment you had assumed management wanted you to work together. This puts it in their court to own up to creating weird internal competition or leaving you to work together like professionals. This can be done immediately or at an early milestone delivery.
Don't play - Approach your manager and say that you have no interest in working independently on a project parallel to this other team but would be ok working with them to deliver the best product possible. This is risky in that it can lead you into ultimatum territory if management pushes back that they want both but maybe this is a good hill to die on (metaphorically speaking).