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badger comments on Single player extensive-form games as a model of UDT - Less Wrong
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Your description of incomplete information is off. What you give as the definition of incomplete information is one type of imperfect information, where nature is added as a player.
A game has incomplete information when one player has more information than another about payoffs. Since Harsanyi, incomplete information has been seen as a special case of imperfect information with nature randomly assigning types to each player according to a commonly known distribution and payoffs given types being commonly known.
Thanks, you're right and I didn't understand what the Harsanyi transformation was. Edited the post again.