  Mean field games (MFGs) and the best reply strategy (BRS) are two methods of
describing competitive optimisation of systems of interacting agents. The
latter can be interpreted as an approximation of the respective MFG system. In
this paper we present a systematic analysis and comparison of the two
approaches in the stationary case. We provide novel existence and uniqueness
results for the stationary boundary value problems related to the MFG and BRS
formulations, and we present an analytical and numerical comparison of the two
paradigms in a variety of modelling situations.
