Is it legal for two companies to sign an agreement saying they will keep their price for a certain product or service the same? Is there a name for this?
It's not legal! against antitrust law unless it's government proved..in which case there's nothing you can do to change that.
Well.....it depends on whether you are in the United States or not. I know over here it's illegal to set prices, especially in writing, but it happens informally all the time. In other countries, you'd have to check with your own laws and what not. Regardless, it would be wise to consult with an attorney rather than asking for legal advice on a public webmaster forum.
It can be legal by setting one company as an affiliate and giving the commission/profit not relatively equal to the original company.