Assuming that you have your home listed with a Realtor, you should have a list of homes that are your main competition. Whenever I am counseling a client we always look at the market from the buyer's perspective. What other homes are they looking at and how do we compare?
The other major factor is market time. The most showing activity occurs in the first two weeks on the market, so if the offer is the first one and you have been on the market a couple of weeks, chances are the offer it probably very close to market value. Most home owners overestimate the value of their property.
I would recommend asking your Realtor to talk with the buyer's agent. Ask them how long they have been looking, have they made any other offers, what other homes have they seen in the area (see if any of your primary competition comes up...it should). From those questions your Realtor should be able to determine if they really think that the offer is a fair one, or if they are low-balling you just to see what you will do.
Buyers that are serious (and these folks did write an offer), working with a Realtor that presents the offer that is complete (proof of downpayment, pre-approval letter, earnest money deposit, etc.) should be taken seriously. Buyers who are in the hunt for a home probably have a pretty good idea of market value.
OTOH, if you are selling without professional representation, you are facing some more significant challenges because you will not know the market data that will tell you if the buyers are just playing games.