  In this paper, under continuity of state-action dynamics, we establish a
large deviations principle (LDP) for discrete-time mean-field games. The proof
is based on transferring LDP for empirical measures of initial states and noise
variables 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.
