  We consider graph games of infinite duration with winning conditions in
parameterized linear temporal logic, where the temporal operators are equipped
with variables for time bounds. In model checking such specifications were
introduced as "PLTL" by Alur et al. and (in a different version called
"PROMPT-LTL") by Kupferman et al..
  We present an algorithm to determine optimal variable valuations that allow a
player to win a game. Furthermore, we show how to determine whether a player
wins a game with respect to some, infinitely many, or all valuations. All our
algorithms run in doubly-exponential time; so, adding bounded temporal
operators does not increase the complexity compared to solving plain LTL games.
