  A symmetric equilibrium in a large game with a convergent sequence of
finite-player games can induce a strategy profile for each finite-player game
in the sequence in an obvious way. We show that such obviously induced strategy
profiles form approximate symmetric equilibria for the sequence of
finite-player games under a continuity assumption. This result demonstrates
from a new angle that large games serve as a reasonable idealization for games
with large but finitely many players. Furthermore, we show that for a large
game with a convergent sequence of finite-player games, the limit distribution
of any convergent sequence of (randomized) approximate equilibria in the
corresponding finite-player games is induced by a symmetric equilibrium in the
limit large game. Various results in the earlier literature on the relevant
closed graph property in the case of pure strategies can be unified under such
a general convergence result. Applications in congestion games are also
presented.
