Games with perfect but incomplete information in real life
A classical example of a game with perfect but incomplete information is an English auction. We know what all the bids have been up to this point but we don't know everyone's valuation of the good being auctioned.

In general, formulating a strategy in this case involves some beliefs about your opponents' payoffs. Typically these are exogenous to the game but I guess you could have some revealed preference throughout an extensive game.