So you've sent out your submission to a few agents and more than one has asked to see a full manuscript or they have otherwise indicated that they're interested in your work. This is, obviously, a Very Nice Position to be in.
Then one of the agents who has progressed to this next stage offers representation. Obviously, that's great because representation is what you wanted. But that doesn't mean you should accept the offer without telling the other agent/s who is/are considering your work. The polite thing to do - and, as I've mentioned before, publishing is a polite industry - is to let the other agent/s know that you've been offered representation and ask them to let you know within a certain time frame if they're interested in doing the same. Keep the time frame short, like a week.
There are a few other reasons why it's wise to do this:
1. It is the professional thing to do. If you were interested in buying a house and you'd looked at it a few times and had inspections done and talked to the real estate agent and mulled over the price you wanted to offer and talked to people about it, wouldn't you be somewhat annoyed if the agent then called you and said the house had been sold to someone else without giving you the chance to even make an offer? Wouldn't you think the sellers were a bit silly because maybe your offer would have been better than they one they accepted? Wouldn't you be upset about the time you'd wasted when you could have been looking at other houses?
2. Karma. If you behave unprofessionally right from this very first stage it can really screw up your karma for the book (I'm serious about this - I've seen it happen).
3. How do you know you went with the right agent? By not giving another interested agent a chance to talk to you about your work and to offer to represent it, how do you know you're with the right agent for you? The agent–author relationship can last for years and, as with any such business relationship, there are several elements to making it work. It needs to be the right fit. So if you have the chance of auditioning a few suitors before making a selection, why wouldn't you?
4. If you do this, and other authors do this, agents may become more wary about submissions. It's hard enough now for agents to keep up with submissions. If enough authors do the ol' 'I've gone with someone else, sucker' routine, we may just abandon them altogether and get our weekends back. So, as a civic service to your fellow writers, please remember that your behaviour reflects on all of them. Because until we get to you know, you're one amorphous pack - just as agents clearly are to you, which is why you went with the first one to materialise as a real person.