Some multi-agent scenarios call for the possibility of evaluating specifications in a richer domain of truth values. Examples include runtime monitoring of a temporal property over a growing prefix of an infinite path, inconsistency analysis in distributed databases, and verification methods that use incomplete anytime algorithms, such as bounded model checking. In this paper, we present multi-valued alternating-time temporal logic (mv-ATL^*_→), an expressive logic to specify strategic abilities in multi-agent systems. It is well known that, for branching-time logics, a general method for model-independent translation from multi-valued to two-valued model checking exists. We show that the method cannot be directly extended to mv-ATL^*_→. We also propose two ways of overcoming the problem. Firstly, we identify constraints on formulas for which the model-independent translation can be suitably adapted. Secondly, we present a model-dependent reduction that can be applied to all formulas of mv-ATL^*_→. We show that, in all cases, the complexity of verification increases only linearly when new truth values are added to the evaluation domain. We also consider several examples that show possible applications of mv-ATL^*_→ and motivate its use for model checking multi-agent systems.