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.

@article{paperbot1666,
  title = {One-Clock Priced Timed Games with Negative Weights},
  author = {Thomas Brihaye and Gilles Geeraerts and Axel Haddad and Engel Lefaucheux and Benjamin Monmege},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 18, Issue 3},
  year = {2022},
  doi = {10.46298/lmcs-18(3:17)2022}
}