A myopic adjustment process for mean field games with finite state and action space

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 is the complexity of the computations necessary to determine dynamic mean field equilibria, which makes it seem questionable whether agents are indeed able to play these equilibria. We prove that the myopic adjustment process converges locally towards strict stationary equilibria under rather broad conditions. Moreover, we also obtain a global convergence result under stronger, yet intuitive conditions.