Mikhail Kalinin was (nominal) Head of State of USSR (Chairman of the Presidium of the Supreme Soviet of the USSR). Stalin generally held all the real power. However all players would expect to see Stalin somewhere in the game, imagine USSR ruled by Molotov and Kalinin

In communist countries there was usually a duplicate hierarchy of the communist party at all levels of government, and it was the head of the party that ruled, though officially there would be some presidents, prime ministers etc. but all would be under the yoke of secretary general of the communist party. It's hard to represent this in the game, where there is only place for government people.