Competing Offer coming in... How can I get an edge?

I haven't put an offer down but want to. The numbers work. I don't want to over pay though. And am so what relieved there's another offer coming in (shows there's demand).

There's the seller's agent and I don't have a buyer's agent (yet).

Is there a way I can get an edge? I was thinking of using the listing agent as my buyer's agent. Is there a way I can figure out what the other offer is?

I just don't want to overpay and want a good deal. I can also use my good friend as the buyers agent (broker) and we split the commission.