There are many possibilities. Here is a pretty simple one to set up:

If one and only one of the proteins has a unique affinity tag, you can use affinity precipitation with a resin or some similar technique to see which protein is bound to the one with the tag.

For example, suppose protein A has a His-tag but proteins B and C do not. If proteins A and B bind each other, a nickel resin can be used to pull down the complex of A and B. If C displaces B from A, then the resin will pull down the AC complex, leaving B in the supernatant.

Hi Devi, you need to provide a bit more detail about your system.

To me, this doesn't sound like classical competitive binding, in which you have 2 proteins with different affinities competing for the same binding site.

You have a third protein that binds to a protein in your complex and dissociates it. This sounds more like allosteric effects than direct competition. 

Also, to me, you could be looking at  two different things going on: 1) binding of the third protein to the complex and 2) dissociation of the complex upon binding of the third protein.

 Hi Devi,

Did you find the protocol for protein competition binding assay? How do you fix your question? I have the same problem. 

Thanks.

Pengfei