Can a retail complex association have a non compete agreement?

I'm not sure what the yogurt guy is talking about.  Restrictive covenants in shopping centers are not uncommon.  For example, before a bakery moves into a shopping center, it might seek a lease provision which prohibits the landlord from renting to any other tenant which will offer fresh baked goods. HOWEVER, you would need such a lease provision BEFORE the landlord rented out the other space.  Absent such a lease provision, there is nothing (assuming no zoning problems) to prohibit the owner from renting to a competing business.  In other words, absent some previous agreement, the other owner is under no obligation to provide a non-compete if he doesn't want to.