  We study graphs and two-player games in which rewards are assigned to states,
and the goal of the players is to satisfy or dissatisfy certain property of the
generated outcome, given as a mean payoff property. Since the notion of
mean-payoff does not reflect possible fluctuations from the mean-payoff along a
run, we propose definitions and algorithms for capturing the stability of the
system, and give algorithms for deciding if a given mean payoff and stability
objective can be ensured in the system
