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:

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> Prince of Persia: The Sands of Time is a film loosely based on the game.
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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: 
Yes. The 2010 movie ***Prince of Persia: The Sands of Time*** was based on the 2003 video game of the same name.

[From Wikipedia](https://en.wikipedia.org/wiki/Prince_of_Persia:_The_Sands_of_Time_(film)#Production):

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> 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. Under John August as executive producer, the series' creator Jordan Mechner was hired to write the script. Producer Jerry Bruckheimer's Pirates of the Caribbean film trilogy served as a touchstone in how a theme park ride was converted into a film franchise. According to Mechner, "Rather than do a straight beat-for-beat adaptation of the new videogame, we're taking some cool elements from the game and using them to craft a new story." Mechner previously considered producing an animated film based on the games, but could not resist Disney and Bruckheimer's offer. In February 2006, Disney hired screenwriter Jeffrey Nachmanoff to write a new script for Prince of Persia.
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So much so that Director Mike Newell had ["an assistant playing the video games to brief him on key details."](http://editorial.rottentomatoes.com/article/mike-newell-drops-early-prince-of-persia-details/)

While based on the game, the movie is not a straight adaptation.
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.

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> 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)
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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.