Evolution of three equity norms of distributive justice in an extended Nash demand game

The Nash demand game (NDG) has been applied to explain moral norms of distributive justice. Skyrms showed a game theoretic explanation of how norms of the equal division could have evolved by using replicator dynamics of NDG. Skyrmsian approach is evolutionary generalist as it entirely omits the psychological mechanisms, in contrast to evolutionary psychology, which emphasizes particular psychological factors of human behaviors. We propose the demand-intensity game (D-I game), which adds an “intensity” dimension to NDG in order to discuss various scenarios for the evolution of norms concerning distributive justice. We present a basic game theory analysis of the D-I game and evolutionary simulations. Three types of norms, libertarianism, “wimpy” libertarianism and egalitarianism could emerge in increasing order of the cost parameter of the game. We also show quasi stability of egalitarian strategies in the game theory analysis, the evolutionary simulation and replicator dynamics. We believe that the D-I game provides us with a useful framework to study dynamics of distributive justice from an emergence perspective, beyond the question of whether strategies demanding an equal share can dominate the population or not.