You'll be able to tell rather quickly, if the property goes "under contract" and shows up as "contingent" or "pending". If a week or two goes by, it would be worth calling the listing agency and inquiring about what's going on.
Homes that are priced well and are attractive to the market for one reason or another (maybe even needing a lot of work) go fast. Some wait for a while.
It doesn't mean there are games being played. This happens. However, it is not required to disclose multiple offers or even that there are other offers. In most cases, it is a good idea, because you get the best deal for the client, but there are two sides to every coin. Not required at all.
Keep your eye on the property. Sometimes offers don't go through. Put yours in as a back up and keep looking. There is a lot out there. It may sound trite, but maybe this was not the house for you, even though you wanted it to be. Your house may be waiting for you to find it.
What are you looking for in a house and what area? I have a friend who is looking to sell a 5 bedroom 2 bath house near Beverly for $175,000. The house has been recently rehabbed and has high end finishes. If your interested contact me or if you have any questions. Also feel free to pass along this information if you know of someone that would be interested in this house.