Mr. Lockhart is generally correct. Although the larger company cannot require these subcontractors to sign a contract saying that they will not work for you, it does not have to hire them, either. There behavior of refusing to deal with anyone dealing with you may be considered monopolizing behavior, and you may want to consult with an anti-trust attorney.
My concern is whether these "subcontractors" really are that or employees. It sounds to me as if you tell them what to sell and when to work. They are engaged in your primary line of work: they do your selling for you. If you have misclassified them as subcontractors, you are subject to a fine, and you will face tax, workers compensation, unemployment, and wage consequences. Assuming these subcontractors are individuals, the only way I can see that they could in fact be true independent contractors would be if you allowed them to set their own prices.
I agree with my colleagues. And even if the activity is not "illegal", there may be a cause of action such as tortuous interference with a business relationship. There may be additional causes if the entertainment venue is a "state" owned enterprise. You should consult with a litigation attorney who can listen to all of the facts and give you a legal opinion.