One way to find this information is by looking through the different versions of the file. You can look at a relevant [help page](https://www.dropbox.com/help/11) of the Dropbox service. Here is an exerp that will get you going:

1. Sign in to the [Dropbox](https://www.dropbox.com) website
2. Right-click on the file in the file browser and select **Previous versions** in the pop-up menu

It's as simple as that. You'll see all the versions and who's been changing it. 

You probably need to have that feature enabled, though. 

**Edit:**

Another way you could find out is by using the **Event tab** from the Dropbox website. You can use the drop-down-list at the top of the page to select the desired shared folder. 

Thanks to the answer [here](http://superuser.com/questions/879528/how-do-i-know-if-dropbox-has-finished-uploading-my-files-from-the-web-interface/879535#879535) for the pointer.