Know your market. I don't know the bay area, assuming you are working with an experienced agent I would expect that you and your agent would have a strategy planning meeting. Having survived the LA hot housing market (being one of 37 offers...not accepted BTW) in one transaction, my advice is to know what is available on the market, and know the value of what is being sold.
Our office had a listing a few months ago that sold with multiple offers because it priced low intentionally. There are reasons that listing agents have for pricing properties. Assuming they are working for the seller's best interest, there are times when underpricing is preferred.
Regardless of multiple offers, if you know the market, you know the value of a given property.
A good agent will do a little detective work and can find out why the home is being sold, when they need to sell, etc. (if I am the listing agent...not from me...unless it is to my seller's benefit).
However, once you know those answers, then you can decide if you want to play the game. Depending upon your goals, if you just "have to have this house" in a certian neighborhood, and (recall the a home purchase is emotional), I ask my buyers :
1. How much are you willing/able to pay
2. What is the alternative if you don't get the house?
Sometimes (schools, it's a house right next to my best friend), you just go in a play your best hand. If I can arrange for the sellers to meet my buyers, then I have a better opportunity. I have the buyers write a nice, handwritten letter, with a family picture, not only a pre-approval, but approval letter that reads: if the house appraises, my buyers get the loan", no other contingencies.
Lastly, I insist on presenting the offer personally to I can answer questions the sellers may have and have the buyers vote of confidence to "make it work".
I want to also know the listing agent. That's why agents that are "in the market" like having transactions with me, because they know the quality of my work. Even if a "better offer" comes in, if it comes down to "who can close escrow" and "who can I trust", agent to agent relationships are key.