The robustness analysis of probabilistic models has been recently the research focus towards verifying the extent to which a system is robust against adversaries, as well as for synthesizing worst-case attacks. In addition to the progress achieved in this direction, a system also needs to exhibit resilience against behaviors that undermine its balance in terms of properties referring to quantitative rewards, such as power consumption, work load or other measurable characteristics. In this paper, we introduce a robustness analysis framework for reward properties over Markov decision processes (MDPs). Apart from the problem of adversarial robustness, we also consider the case of strategic entities who seek to maximize their influence in the convergence of network-based systems. To this end, our robustness framework features an infinite horizon analysis for irreducible MDPs.