Outsourced computing is increasingly popular thanks to the effectiveness and convenience of cloud computing -as-a-Service offerings. However, cloud nodes can potentially misbehave in order to save resources. As such, some guarantee over the correctness and availability of results is needed. Exploiting the redundancy of cloud nodes can be of help, even though smart cheating strategies render the detection and correction of fake results much harder to achieve in practice. In this paper, we analyze the above issues and provide a solution for a specific problem that, nevertheless, is quite representative for a generic class of problems in the above setting: computing a vectorial function over a set of nodes. In particular, we introduce AntiCheetah, a novel autonomic multi-round approach performing the assignment of input elements to cloud nodes as an autonomic, self-configuring and self-optimizing cloud system. AntiCheetah is resilient against misbehaving nodes, and it is effective even in worst-case scenarios and against smart cheaters that behave according to complex strategies. Further, we discuss benefits and pitfalls of the AntiCheetah approach in different scenarios. Preliminary experimental results over a custom-built, scalable, and flexible simulator (SofA) show the quality and viability of our solution.