Two-player zero-sum games are a well-established model for synthesising
controllers that optimise some performance criterion. In such games one player
represents the controller, while the other describes the (adversarial)
environment, and controller synthesis corresponds to computing the optimal
strategies of the controller for a given criterion. Asarin and Maler initiated
the study of quantitative games on (non-probabilistic) timed automata by
synthesising controllers which optimise the time to reach a final state.
An average-time game is played on the infinite graph of configurations of a
finite timed automaton. The two players, Min and Max, construct an infinite run
of the automaton by taking turns to perform a timed transition. Player Min
wants to minimise the average time per transition and player Max wants to
maximise it. A solution of average-time games is presented using a reduction to
average-price game on a finite graph. A direct consequence is an elementary
proof of determinacy for average-time games.