  We study the problem of formalizing and checking probabilistic
hyperproperties for models that allow nondeterminism in actions. We extend the
temporal logic \HyperPCTL, which has been previously introduced for
discrete-time Markov chains, to enable the specification of hyperproperties
also for Markov decision processes. We generalize HyperPCTL by allowing
explicit and simultaneous quantification over schedulers and probabilistic
computation trees and show that it can express important quantitative
requirements in security and privacy. We show that HyperPCTL model checking
over MDPs is in general undecidable for quantification over probabilistic
schedulers with memory, but restricting the domain to memoryless
non-probabilistic schedulers turns the model checking problem decidable.
Subsequently, we propose an SMT-based encoding for model checking this language
and evaluate its performance.
