I was curious, so I did some research and here is what I found:

I believe they were Sultans until the Shi'ite's took over (at which time the term Shah was used) (Unless the history below is incorrect) This may help:

The Persian Empire is one of the oldest monarchies in the world. It dates from the middle of the 6th century BC when Cyrus II, King of Anshan succeeded in conquering his Lydia and Babylon. His successors vastly increased their territories, conquering Egypt and large parts of Asia and the Middle East, eventually even threatening Greece and Europe. The defeat of Darius III by Alexander the Great is now a matter of legend. Dynasty followed dynasty, Arsac, Seleucid, and Sassanian, in an historic tapestry too rich to elucidate here. The last Sassanian King succumbed to an assassin and the Empire fell to the Caliphate of the new Muslim religion in 642 AD. Wrested from the Caliphs by the Seljuqs in 1040, Persia continued under the rule of the latter until the early 12th century. A long period of disintegration into small independent and semi-independent local states then ensued until conquest by the Mongol Horde led by Jenghiz Khan. His descendants established an independent Empire once more, which lasted until 1335. A further period of disintegration was ended by its conquest by Timur Gughan Sahib-i-Kiran (Tamerlane) in 1393. His Timurid successors ruling until the conquest of the Turkoman tribes around 1450. The Qara Quyunlu (black sheep) tribe or dynasty ruling until their replacement by the Aq Quyunlu (white sheep) in 1468. The latter ruled Persia for the rest of the 15th century until falling to the Shi'ite onslaught of the Qizilbashi (red hats). Their leader and the Grand Master of the Sufi Order, Ismail Safawi, was proclaimed Shah on the fall of Isfahan in 1501.

The term Sultan was in use until the advent of the Pahlavi regime:

The earliest verifiable ancestor of the Pahlavi family was Captain Morad Ali Khan. His grandson, Reza Khan was brought to power in a coup d'etat in 1921. The Qajar dynasty was ousted and Reza Khan proclaimed as Shahanshah by the Persian Majlis in 1925. The name of the country was altered to Iran (Land of the Aryans) in 1935. His son and successor, Muhammad Reza Shah, was forced into self-imposed exile by the Islamic revolution in 1979, Iran was proclaimed an Islamic Republic and the monarchy was abolished.


Tracy

>>>"In ancient Persia there lived a Sultan who had an only daughter..." (Game "Prince of Persia - 2", introductory screen).
>>>
>>>How could such a disaster ever happen?
>>>
>>>Hilmar.
>>
>>My guess would be that people who could "help" were too afraid of him. :)
>
>I meant another type of disaster: the fact that the game designers placed a Sultan (rather than a Shah) on the throne of ancient Persia.
>
>Hilmar.