Question: I heard that [Prince of Persia: The sands of time movie](http://en.wikipedia.org/wiki/Prince_of_Persia%3a_The_Sands_of_Time_%28film%29) was based on the [Prince of Persia: The sands of time video game](http://en.wikipedia.org/wiki/Prince_of_Persia%3a_The_Sands_of_Time). However in the wiki article it is said:

> 
> Prince of Persia: The Sands of Time is a film loosely based on the game.
> 
> 
> 

I also found that the writers of the movie are Jordan Mechner, Boaz Yakin, Doug Miro. I am not aware of the story of the game. So is the story of the film not the same as that of the game? Also I could not see any attribute in the film to the game. So did the producers not buy the story legally from Ubisoft? What is the back story?

Answer: 
As an addition to *Tyler*'s answer, while the story, the locations, the characters and their particular relationships are different from the game, there are still many general similarities in the story development of both the movie and the video game, apart from the obvious presence of the *"Sand of Time"*, the dagger and the *"Prince of Persia"* himself:

Similar to the movie the *Vezier* (though not being related to the *Prince*'s family) more or less persuades the *Prince*'s father to conquer a realm for more or less normal reasons (game: wealth and honor, movie: preemptive attack) just to secretly get his hands on the *Sand of Time*. The *Prince* in turn tries to impress his father, and steals the *Dagger of Time* during this attack (not knowing what it can do), much to the dismay of the *Vezier*'s evil plans.

On his way to correct things (though in the game everybody is dead/evil and in the movie he is merely banned/wanted for betrayal), he meets a girl who in the end knows much more about the *Sand* and the *Dagger*. She wants to get her hands on it in order to correct things, while the *Prince* is rather stubborn, doesn't trust her and wants to do things his own way by keeping the dagger getting both into conflict.

At the end, they manage to find the source of the *Sand of Time*, and by reuniting it with the *Dagger*, turn back the time to the start of the adventure. The *Prince* gets the chance to prevent all those evil things happening, and just hints at the girl (who has no memory of her adventure in the other timeline) as to what actually happened.

So while the story is quite different, major plot elements along with the general personalities and relationships of the major characters are not that dissimilar between the movie and the game.
As per your production rite question, the answer is yes they brought the rights , As per [Wiki statement](http://en.wikipedia.org/wiki/Prince_of_Persia:_The_Sands_of_Time_%28film%29)- 

> 
> In March 2004, the production company Jerry Bruckheimer Films sought
>  to acquire feature film rights to the 2003 video game Prince of
>  Persia: The Sands of Time with the film to be distributed by Walt
>  Disney Pictures.
> 
> 
> 

And giving attribute to game depends on the agreement terms and condition. And I think their is no need to give attribute if you brought the full rights.

The movie is just loosely based on the Prince of Persia: The Sands of Time and Elements from Prince of Persia: Warrior Within and Prince of Persia: The Two Thrones are also incorporated in it.

> 
> Mechner, in writing the script, re-conceived the storyline to shift
>  the perspective from the interactive one experienced by video gamers
>  to the non-interactive experience by film audiences. The screenwriter
>  left out elements of the Prince of Persia video games Warrior Within
>  and The Two Thrones and did not anticipate including these elements in
>  the film's possible sequels. [(source)](http://en.wikipedia.org/wiki/Prince_of_Persia:_The_Sands_of_Time_%28film%29)
> 
> 
> 

Rather then explaining all the differences, we can only say that its story retelling by just taking some of characters but with different origin stories and little different situation. They removed the context of sand storm and monster and just made the movie full of more human rather the sand monsters. Other major differences are the death of king in different way, completely different princess story (princess is a prisoner in the game), Vezir's have no relation to king in the game, an extra character brother of prince and different love story too. In the game prince doesn't trust the princess because of the wrong treatment to her by his own kingdom and she earned the trust later in the game.