  Recently, in [K.R. Apt and S. Simon: Well-founded extensive games with
perfect information, TARK21], we studied well-founded games, a natural
extension of finite extensive games with perfect information in which all plays
are finite. We extend here, to this class of games, two results concerned with
iterated elimination of weakly dominated strategies, originally established for
finite extensive games.
  The first one states that every finite extensive game with perfect
information and injective payoff functions can be reduced by a specific
iterated elimination of weakly dominated strategies to a trivial game
containing the unique subgame perfect equilibrium. Our extension of this result
to well-founded games admits transfinite iterated elimination of strategies. It
applies to an infinite version of the centipede game. It also generalizes the
original result to a class of finite games that may have several subgame
perfect equilibria.
  The second one states that finite zero-sum games with 'n' outcomes can be
solved by the maximal iterated elimination of weakly dominated strategies in
'n-1' steps. We generalize this result to a natural class of well-founded
strictly competitive games.
