  In this paper, we establish a large deviations principle (LDP) for
interacting particle systems that arise from state and action dynamics of
discrete-time mean-field games under the equilibrium policy of the
infinite-population limit. The LDP is proved under weak Feller continuity of
state and action dynamics. The proof is based on transferring LDP for empirical
measures of initial states and noise variables under setwise topology to the
original game model via contraction principle, which was first suggested by
Delarue, Lacker, and Ramanan to establish LDP for continuous-time mean-field
games under common noise. We also compare our work with LDP results established
in prior literature for interacting particle systems, which are in a sense
uncontrolled versions of mean-field games.
