Formal definition of perfect information I am looking for the formal definition of 'perfect information' in game theory.

Please direct me to a book or preferably an online paper where I can find it.

On a related note:
The Wikipedia page for the term is not very useful. It only offers an informal definition:


  In game theory, an extensive-form game has perfect information if each player, when making any decision, is perfectly informed of all the events that have previously occurred


Given this definition the simultaneous move examples seem strange. The games mentioned (e.g. iterated prisoner's dilemma) could easily be altered to have sequential moves where the second mover is simply not aware of the first move. This game would have the same extensive form but would no longer fit the informal definition.
A simultaneous-move game is not a game of perfect information. It is a game of imperfect information.

Let me quote Gibbons (Chapter 2, p.58).


  The key features of a dynamic game of complete and perfect information are
  that 
   (i) the moves occur in sequence, 
   (ii) all previous moves are observed before the next move is chosen, and 
   (iii) the players' payoffs from each feasible combination of moves are common knowledge.


Picking up the discussion in the comments, let me again quote Gibbons, p.122, Footnote 19:


  This characterization of perfect and imperfect information in terms of singleton
  and nonsingleton information sets is restricted to games of complete information
  because, as we will see in Chapter 4, the extensive-form representation of
  a game with perfect but incomplete information has a nonsingleton information
  set. In this chapter, however, we restrict attention to complete information.