  In this paper we present different applications of finite state mean field
games to socio-economic sciences. Examples include paradigm shifts in the
scientific community or the consumer choice behaviour in the free market. The
corresponding finite state mean field game models are hyperbolic systems of
partial differential equations, for which we present and validate different
numerical methods. We illustrate the behaviour of solutions with various
numerical experiments, which show interesting phenomena like shock formation.
Hence we conclude with an investigation of the shock structure in the case of
two-state problems.
