  Priced timed games are two-player zero-sum games played on priced timed
automata (whose locations and transitions are labeled by weights modelling the
cost of spending time in a state and executing an action, respectively). The
goals of the players are to minimise and maximise the cost to reach a target
location, respectively. We consider priced timed games with one clock and
arbitrary integer weights and show that, for an important subclass of them (the
so-called simple priced timed games), one can compute, in pseudo-polynomial
time, the optimal values that the players can achieve, with their associated
optimal strategies. As side results, we also show that one-clock priced timed
games are determined and that we can use our result on simple priced timed
games to solve the more general class of so-called negative-reset-acyclic
priced timed games (with arbitrary integer weights and one clock). The
decidability status of the full class of priced timed games with one-clock and
arbitrary integer weights still remains open.
