You can buy and sell country .edu domains. But that type domains are at the black side at the search engines databases, you cant get any rep for that domain/websites for Google,Yahoo results..
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Perhaps you are referring to your own subdomain or blog/forum on a .edu domain... It is quite common for students to have access to post their own blog or forum on their university or college website.
I have often wondered what these are worth or how they can be utilized properly. However I have come to the understand that they cannot be bought and sold. In addition any SEO benefit is pretty much dead as everyone and their brother have Googled for ".edu and .gov backlinks" spamming them beyond belief.
If you do own a .edu on its own I would inquire how you were able to acquire it and what corresponding school you own.
For leasing or sell domain names to another is simple. But .edu might be registered by institutions who own it. if someone does it for their institutions, i believe they never sell it. if someone wants to do it they may be sold their institutions with the domain name. But i don't understand that an individual has a .edu domain.
.edu domains from 2001 and earlier are grandfathered.
But they cannot be traded, the only way would be to sell the 'school' or whatever body the domain was awarded to.
If it was registered to an individual you may be out of luck. Or the prospective buyer should consider a name change... possibly change of gender too :gl: