As long as all four are set up as agents, and they are all part of the same Group set up within your Department, they should all see any ticket that comes in. Distribution method determines how those tickets are distributed: either automatically (via Round Robin) or agents can pull tickets individually (or cherry pick them). Tickets can only be "owned" by an individual agent, thought tickets can be transferred between agents, or an agent can take a ticket from another agent. 

This Help page may help explain this:

Company Organization: https://help.smartertools.com/SmarterTrack/Current/Topics/Concepts/CompanyOrg

Thank you for your response. When a ticket comes in all can see it in the group, I understand that. All four members are agents, once the ticket is assigned to an agent, can the other three remaining agents see that ticket or no because it is assigned specifically to another agent?

Thank you for the information, it is much appreciated.