  We introduce consumption games, a model for discrete interactive system with
multiple resources that are consumed or reloaded independently. More precisely,
a consumption game is a finite-state graph where each transition is labeled by
a vector of resource updates, where every update is a non-positive number or
omega. The omega updates model the reloading of a given resource. Each vertex
belongs either to player \Box or player \Diamond, where the aim of player \Box
is to play so that the resources are never exhausted. We consider several
natural algorithmic problems about consumption games, and show that although
these problems are computationally hard in general, they are solvable in
polynomial time for every fixed number of resource types (i.e., the dimension
of the update vectors).

Computer Science and Game Theory;Systems and Control;Optimization and Control