> A free market is defined as an exchange where both sides have access to the same information.

Its free as in freedom; to do anything. You are free to ask anyone about anything anytime.

You can do anything except be physical aggresive (like states).

> Even fervent laissez-faire economists admit the necessity of appropriate regulations: contract enforcement rules, avoidance of monopolies, a system of law and order for handling disputes, etc.

All of these has free market solutions.

All of these peope you speak of are not free market supporters. They are statists.