Group Fairness and Game Theory

In this paper I extend Matthew Rabins model of fairness equilibria (1993) to groups of individuals. This allow me to introduce three aspects from reality that are absent in game theory: i) individuals discriminate in favor of members of their own groups, ii) individuals like individuals that not only are kind to them, but are kind to other individuals, specially individuals of their own groups, and iii) individuals discrimate in favor of members of groups they like. I define a new equilibrium that takes in consideration this emotions, what I call group fairness equilibrium. Rabin defines the mutual-max outcomes for a single game as outcomes where each player maximize the other players material mayoffs and the mutual-min outcomes as outcomes where each player minimize the other players material payoffs. Some basic results of my model are that a combination of strict Nash equilibrium in several games, will always be a group fairness equibrium for large values of the material payoffs, and that any outcome that is either strictly mutual-max for both games or strictly mutual-min for both games is a group fairness equilibrium for large values of the material payoffs.