  The most popular stability notion in games should be Nash equilibrium under
the rationality of players who maximize their own payoff individually. In
contrast, in many scenarios, players can be (partly) irrational with some
unpredictable factors. Hence a strategy profile can be more robust if it is
resilient against certain irrational behaviors. In this paper, we propose a
stability notion that is resilient against envy. A strategy profile is said to
be envy-proof if each player cannot gain a competitive edge with respect to the
change in utility over the other players by deviation. Together with Nash
equilibrium and another stability notion called immunity, we show how these
separate notions are related to each other, whether they exist in games, and
whether and when a strategy profile satisfying these notions can be efficiently
found. We answer these questions by starting with the general two player game
and extend the discussion for the approximate stability and for the
corresponding fault-tolerance notions in multi-player games.
