  In a society of completely selfish individuals where everybody is only
interested in maximizing his own payoff, does any equilibrium exist for the
society? John Nash proved more than 50 years ago that an equilibrium always
exists such that nobody would benefit from unilaterally changing his strategy.
Nash Equilibrium is a central concept in game theory, which offers a
mathematical foundation for social science and economy. However, it is
important from both a theoretical and a practical point of view to understand
game playing where individuals are less selfish. This paper offers a
constructive generalization of Nash equilibrium to study n-person games where
the selfishness of individuals can be defined at any level, including the
extreme of complete selfishness. The generalization is constructive since it
offers a protocol for individuals in a society to reach an equilibrium. Most
importantly, this paper presents experimental results and theoretical
investigation to show that the individuals in a society can reduce their
selfishness level together to reach a new equilibrium where they can have
better payoffs and the society is more stable at the same time. This study
suggests that, for the benefit of everyone in a society (including the
financial market), the pursuit of maximal payoff by each individual should be
controlled at some level either by voluntary good citizenship or by imposed
regulations.
