Yes, your competitors may be allowed to do some trades. To enable this option, in the General rules, choose the desired trade type.  Then, a link called "Trade rules" will appear in the left navigation bar.  Click on it to get all the details regarding trading on PoolExpert.

DO NOT set any trade periods here if you wish to control all the roster changes yourself.

When trade periods are defined, your competitors will have a link in the toolbar on the left of the page that will bring them to the trade page.

Note: For a competitor to be able to perform a trade by himself, you must specify his e-mail address in his profile and he must connect to the pool using that same address and not by using the quick access.