Evolution of Three Norms of Distributive Justice in an Extended Nash Demand Game

The Nash demand game (NDG) has been at the center of attention when explaining moral norms of distributive justice on the basis of the game theory. This paper describes 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, while keeping such simplicity that it can be analyzed by the concepts and tools of the game theory. We perform an ESS analysis and evolutionary simulations, followed by the analysis of replicator dynamics. It is shown that the three norms emerge: the one claiming an equal distribution ( Egalitarianism ), the one claiming the full amount ( Libertarianism ), and, as the special case of Libertarianism, the one claiming the full amount but conceding the resource in conflict ( Wimpy libertarianism ). The evolution of these norms strongly depends on the conflict cost parameter. Egalitarianism emerges with a larger conflict cost while Libertarianism with a smaller cost. Wimpy libertarianism emerges with a relatively larger conflict cost in libertarianism. The simulation results show that there are three types of evolutionary scenarios in general. We see in most of the trials the population straightforwardly converges to Libertarianism or Egalitarianism. It is also shown that, in some range of the conflict cost, the population nearly converges to Egalitarianism, which is followed by the convergence to Libertarianism. It is shown that this evolutionary transition depends on the quasi stability of Egalitarianism.