Design decisions made during early development stages of self-adaptive systems tend to have a significant impact upon system properties at run time (e.g., safety, QoS). However, understanding the implications of these decisions a priori is difficult due to the different types and degrees of uncertainty that affect such systems (e.g., simplifying assumptions, human-in-the-loop). To provide some assurances about self-adaptive system designs, evidence can be gathered from activities such as simulations and prototyping, but these demand a significant effort and do not provide a systematic way of dealing with uncertainty. In this chapter, we describe an approach based on model checking of stochastic multiplayer games (SMGs) that enables developers to approximate the behavioral envelope of a self-adaptive system by analyzing best- and worst-case scenarios of alternative designs for self-adaptation mechanisms. Compared to other sources of evidence, such as simulations or prototypes, our approach is purely declarative and hence has the potential of providing developers with a preliminary understanding of adaptation behavior with less effort, and without the need to have any specific adaptation algorithms or infrastructure in place. We illustrate our approach by showing how it can be used to mitigate different types of uncertainty in contexts such as self-protecting systems, proactive latency-aware adaptation, and human-in-the-loop adaptation.