We present a framework for game semantics based on concurrent games, that keeps track of resources as data modified throughout execution but not affecting its control flow. Our leading example is time, yet the construction is in fact parametrized by a resource bimonoid R, an algebraic structure expressing resources and the effect of their consumption either sequentially or in parallel. Relying on our construction, we give a sound resource-sensitive denotation to R-IPA, an affine higher-order concurrent programming language with shared state and a primitive for resource consumption in R. Compared with general operational semantics parametrized by R, our resource analysis turns out to be finer, leading to non-adequacy. Yet, our model is not degenerate as adequacy holds for an operational semantics specialized to time. In regard to earlier semantic frameworks for tracking resources, the main novelty of our work is that it is based on a non-interleaving semantics, and as such accounts for parallel use of resources accurately.