If each member has its own private key, then each member must have a corresponding public key. None of these public keys can be identical.
If you want to distribute data from one system to one or more other systems using encryption, please use an existing protocol to do this, like TLS or SSL, as these techniques have been tried and tested and are proven to be secure when configured correctly.
Data decryption for asymmetric ciphers is computationally difficult - the method for distributing large quantities of encrypted data is to only use an asymmetric cipher to negotiate and share a symmetric cipher key. The asymmetric cipher can then be replaced with a symmetric cipher - as both parties now have the shared key. Symmetric cryptography is computationally cheaper and faster than asymmetric.
All your setup requires is that the cluster head maintains a list of public keys for each of your cluster nodes, and when you want to distribute encrypted data to each of them, you encrypt your data for each node separately, using each node's public key. Each node then has access to its own encrypted data block which each can decrypt using its own private key.
To use symmetric crypto in the above example (for each client), you have to generate a new symmetric key, encrypt the data with it, then encrypt the symmetric key itself using the client's public key, and store the encrypted key with the message for the client to download.
This is basically the definition of PKI. Public Key Infrastructure is simply a structured method of managing keys and keypairs to allow secure communication to be performed between systems.