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 minimize the average time per transition and

player Max wants to maximize 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.

This complements our results for reachability-time games and

partially solves a problem posed by Bouyer et al., to design an

algorithm for solving average-price games on priced timed

automata.

The paper also establishes the exact computational complexity of

solving average-time games: the problem is EXPTIME-complete for

timed automata with at least two clocks.