Liberal marriage = middle eastern marriage????

I read a very interesting article today: the wife of a billionaire, whose name I will not mention, has an agreement with her husband: In case of a divorce she will receive US $ 9 million. Pretty good deal, you might think. However, the man has an agreement as well: he can do whatever he wants, including having numerous women on the side. Liberal marriage, you might think.
So, as a pragmatic person I added 1 plus 1 and came to the following conclusion: the woman has sold herself for 9 million dollars.

Then the question came up to my mind: what makes this arrangement any different from the ones middle eastern men have with their wives? Everyone always says that the Islamic religion allows them to have 4 wives (restrictions apply to that, I won't get too much into the details, but as a resume: the 1st wife has to give her permission and there must be reasons for the second marriage). The man has to treat his wives all the same way, which in my opinion is absolutely impossible, since I can not even treat two pairs of my shoes the same! And spend equal amounts of nights with each of them. In some Islamic countries a certain financial agreement are made, which is comparable to a gift from the husband to the wife in case of a divorce.

Now, this western billionaire, who I mentioned above, he obviously has the wife's agreement to have mistress, one night stands and girl friends on the side. Therefore the first check is done.
If he treats them all the same way and spends time with all of them equally is open. Maybe yes, maybe no. Hence: in dubio pro reo.

Now my question; what exactly is the difference between this liberal marriage and the one's people have in the middle east? Could I from now on say that liberal marriages are middle eastern marriages? Sounds pretty funny to me! :)