  Alternating-time temporal logic (ATL$^*$) is a well-established framework for
formal reasoning about multi-agent systems. However, while ATL$^*$ can reason
about the strategic ability of agents (e.g., some coalition $A$ can ensure that
a goal is reached eventually), we cannot compare multiple strategic
interactions, nor can we require multiple agents to follow the same strategy.
For example, we cannot state that coalition $A$ can reach a goal sooner (or
more often) than some other coalition $A'$. In this paper, we propose
HyperATLS$^*_S$, an extension of ATL$^*$ in which we can (1) compare the
outcome of multiple strategic interactions w.r.t. a hyperproperty, i.e., a
property that refers to multiple paths at the same time, and (2) enforce that
some agents share the same strategy. We show that HyperATL$^*_S$ is a rich
specification language that captures important AI-related properties that were
out of reach of existing logics. We prove that model checking of HyperATL$^*_S$
on concurrent game structures is decidable. We implement our model-checking
algorithm in a tool we call HyMASMC and evaluate it on a range of benchmarks.
