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Priced timed games are two-player zero-sum games played on priced timedautomata (whose locations and transitions are labeled by weights modeling thecosts of spending time in a state and executing an action, respectively). Thegoals of the players are to minimise and maximise the cost to reach a targetlocation, respectively. We consider priced timed games with one clock andarbitrary (positive and negative) weights and show that, for an importantsubclass of theirs (the so-called simple priced timed games), one can compute,in exponential time, the optimal values that the players can achieve, withtheir associated optimal strategies. As side results, we also show thatone-clock priced timed games are determined and that we can use our result onsimple priced timed games to solve the more general class of so-calledreset-acyclic priced timed games (with arbitrary weights and one-clock).

Simple Priced Timed Games Are Not That Simple