  In this paper, we introduce a natural learning rule for mean field games with
finite state and action space, the so-called myopic adjustment process. The
main motivation for these considerations are the complex computations necessary
to determine dynamic mean-field equilibria, which make it seem questionable
whether agents are indeed able to play these equilibria. We prove that the
myopic adjustment process converges locally towards stationary equilibria with
deterministic equilibrium strategies under rather broad conditions. Moreover,
for a two-strategy setting, we also obtain a global convergence result under
stronger, yet intuitive conditions.

Optimization and Control;Theoretical Economics