Should negotiations be open to anybody who'd like to participate or should they be behind closed doors? Why?

It should be closed door for equal parties. Because making a good bargain needs surprised elements and a clear vision.  Negotiation should be based on personal with experience. Focus on "give and take" with a winning hands technique. 

Negotiations should be behind closed doors are this is confidential in nature.  Foolowing factors can be viewed as support to this stand:

1.Negotiations basically are between 2 parties i.e. supplier & purchaser.  During the process, confidential information is exchanged about the product & pricing from the supplier's side and quantum and period of supplies by the purchaser.  

2.Respective parties have reservations on profit margin and budget which cannot be made public

3. Certain persons are entrusted with responsibility to negotiate considering their experience, product knowledge and market study.  Not everyone is empowered with the same

4. Negotiations are also about the policy and future plans of the companies which is highly confidential 

Negotiation has to be closed doors with negotiating parties having full and equal representation so as to allow them leverage on their expertise to harness the opportunities therein.

I support making behind closed doors, on the other hand in a professionally managed organisation most issues should be transparent for a good & clear management. 

Negotiations should be closed door activity with team having meaningful representation of the counter party.If an open negotiation is done it will not end up in a solution due to the mass psychology that every individual will perform to prove his capabilities than  solving the issue of group.

yes of course, Negotiation helps to widen the network. by participate whoever likes to, it helps to create network and to improvise the bargaining ability. knowing the client is a more important thing.

Negotiations should be always in closed doors and ensure that the competitor or anyone else in not aware of the rates and terms and conditions.