  We study the inefficiency of equilibria for various classes of games when
players are (partially) altruistic. We model altruistic behavior by assuming
that player i's perceived cost is a convex combination of 1-\alpha_i times his
direct cost and \alpha_i times the social cost. Tuning the parameters \alpha_i
allows smooth interpolation between purely selfish and purely altruistic
behavior. Within this framework, we study altruistic extensions of linear
congestion games, fair cost-sharing games and valid utility games.
  We derive (tight) bounds on the price of anarchy of these games for several
solution concepts. Thereto, we suitably adapt the smoothness notion introduced
by Roughgarden and show that it captures the essential properties to determine
the robust price of anarchy of these games. Our bounds show that for congestion
games and cost-sharing games, the worst-case robust price of anarchy increases
with increasing altruism, while for valid utility games, it remains constant
and is not affected by altruism. However, the increase in the price of anarchy
is not a universal phenomenon: for symmetric singleton linear congestion games,
we derive a bound on the pure price of anarchy that decreases as the level of
altruism increases. Since the bound is also strictly lower than the robust
price of anarchy, it exhibits a natural example in which Nash equilibria are
more efficient than more permissive notions of equilibrium.
