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Network games are widely used as a model for selfish resource-allocationproblems. In the classical model, each player selects a path connecting hersource and target vertices. The cost of traversing an edge depends on the {\emload}; namely, number of players that traverse it. Thus, it abstracts the factthat different users may use a resource at different times and for differentdurations, which plays an important role in determining the costs of the usersin reality. For example, when transmitting packets in a communication network,routing traffic in a road network, or processing a task in a production system,actual sharing and congestion of resources crucially depends on time.  In \cite{AGK17}, we introduced {\em timed network games}, which add a timecomponent to network games. Each vertex $v$ in the network is associated with acost function, mapping the load on $v$ to the price that a player pays forstaying in $v$ for one time unit with this load. Each edge in the network isguarded by the time intervals in which it can be traversed, which forces theplayers to spend time in the vertices. In this work we significantly extend theway time can be referred to in timed network games. In the model we study, thenetwork is equipped with {\em clocks}, and, as in timed automata, edges areguarded by constraints on the values of the clocks, and their traversal mayinvolve a reset of some clocks. We argue that the stronger model captures manyrealistic networks. The addition of clocks breaks the techniques we developedin \cite{AGK17} and we develop new techniques in order to show that positiveresults on classic network games carry over to the stronger timed setting.

Timed Network Games with Clocks