For example, if you are using a literary agent to negotiate with publishers for a book you have written, and a theatrical agent for your theatre work, then each will have his own clearly defined area, and they will not get in each other's way.

Most agents operating in the entertainment industry will not agree to take a potential client onto their books unless they have exclusivity throughout the term of the contract. It is not really neither sensible nor practicable in normal circumstances to set it up differently, because of the awkward problems this can create, such as:

(i) both agents claiming commission for the same 'introduction';
(ii) casting agents and producers not knowing which agent to contact in any given instance if they want to put a new proposal to or obtain information from your 'agent';
(iii) one agent interfering with negotiations being conducted by another, possibly to your detriment;
(iv) each agent blaming the other if things go wrong;
(v) payments and correspondence being misdirected to the wrong agent.

If you have been unwise enough to appoint both as your 'exclusive' agent for the same field of activity, without the agreement of both. Then you will be in breach of contract to both and, depending on the circumstances and how they both react on discovering the true position, you could end up paying double commission, or more likely full commission to the first and damages to the second.

Having more than one 'non-exclusive' agent operating in the same field of activity and the same territory, although usually considered unwise, can nevertheless work perfectly well in two other circumstances.
Apart from the one relating to each agent having his own separate exclusive area of activity or geographical area (for example one in the UK and one in the USA or one for film work and the other for theatre work).

The first is where an agent appoints one or more sub-agents, perhaps in different territories.
Thus, if your agent is in the UK he may have a sub-agent in the USA to look for and negotiate opportunities for you in the latter territory on a commission-sharing basis, but in such circumstances the sub-agent's contractual relationship will be with your main agent and not with you. Indeed, you may not even be aware of the sub-agent's existence. Alternatively, your contract with your agent may allow for this in the commission rates applicable. You should be aware in this context that draft new regulations published by the DTI, will, if brought into effect in their present form, make it illegal for an agency to assign or sub-contract to a third party any of its obligations to a client without the client's consent.

The second situation is where your so-called 'agent' is not really acting as an agent at all, but is operating an 'employment business'. Where under he contracts directly with you in buying your services for a specific engagement, and then sells those services under a separate contract of his own with the venue manager or other end-user.

This is what is called a 'net deal' or 'buy/sell' arrangement.
It means that the 'intermediary' will be responsible for paying the artist even if the venue manager defaults, and even if the intermediary himself never gets paid. Conversely it also means that the intermediary will be personally responsible to the venue manager if the artist defaults and fails to turn up to fulfil the engagement, so that the intermediary will not be able to hide behind agency status.

The intermediary may contract with the artist direct or with the artist's agent, but in either case will be acting as a principal, rather than an agent, so that there is no contract between artist and end-user.
Some artists may prefer to operate freelance, without an exclusive agent as such, leaving themselves free to enter into direct buy/sell agreements on the open market with whoever offers them the best terms, but this is rare and confined to big name artists. They have the confidence and resources to operate in this way because the demand for their services is so high, but the paradox is that they have to accept the time consuming distraction of negotiating terms themselves.