A Constructive Generalization of Nash Equilibrium for Better Payoffs and Stability

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.