Evolution of Three Norms of Distributive Justice in an Extended Nash Demand Game
Kazuaki Kojima and Takaya Arita
Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan
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.
-  J. F. Nash, “The bargaining problem,” Econometrica, Vol.18, pp. 155-162, 1950.
-  J.M. Alexander, “Evolutoinary explanations of distributive justice,” Philosophy of Science, Vol.67, No.3, pp. 490-516, 2000.
-  K. Binmore, “Game Theory and the Social Contract, Vol.2: Just Playing,” The MIT Press, Cambridge, 1998.
-  A. Rubinstein, “Perfect Equilibrium in a Bargaining Model,” Econometrica, Vol.50, pp. 97-109, 1982.
-  B. Skyrms, “Evolution of the Social Contract,” Cambridge University Press, Cambridge, 1996.
-  R. Sugden, “The Economics of Rights, Co-operation and Welfare,” Basil Blackwell, Oxford, 1986.
-  P. H. Young, “An Evolutionary Model of Bargaining,” J. of Economic Theory, Vol.59, No.1, pp. 145-168, 1993.
-  P. H. Young, “Individual Strategy and Social Structure: An Evolutionary Theory,” Princeton University Press, Princeton, 1998.
-  A. Andreozzi, “An evolutionary theory of social justice: Choosing the right game,” European J. of Political Economy, Vol.26, No.3, pp. 320-329, 2010.
-  G. Mar, “Evolutionary game theory, morality, and darwinism,” D. Katz (ed.), Evolutionary Origins of Morality, pp. 322-326, Imprint Academic, 2000.
-  C. T. Dawes, J. H. Fowler, T. Johnson, R. McElreath, and O. Smirnov, “Egalitarian motives in humans,” Nature, Vol.446, pp. 794-796, 2007.
-  M. Hsu, C. Anen, and S. R. Quartz, “The right and the good: dstributive justice and neural encoding of equity and efficency,” Science, Vol.320, pp. 1092-1095, 2008.
-  J. D’Arms, R. Batterman, and K. Górny, “Game theoretic explanations and the evolution of justice,” Philosophy of Science, Vol.65, No.1, pp. 76-102, 1998.
-  H. Ohtsuki, “Evolutionary Dynamics of the Nash Demand Game: A Diffusion Approach,” Dynamic Games and Applications, Vol.1, pp. 449-461, 2011.
-  K. Kojima and T. Arita, “How do equity norms evolve? – An evolutionary game theory approach to distributive justice,” Artificial Life and Robotics, Vol.17, No.2, pp. 287-292, 2012.
-  J. F. Nash, “Two-person Cooperative Games,” Econometrica, Vol.21, pp. 128-140, 1953.
-  S. Nakamura, K. Kojima, R. Suzuki, and T. Arita, “Design of Experiments on a Game Focused on Distributive Justice Using Human Subjects,” Proc. of the SICE 39th Intelligent System Symp., pp. 271-276, 2012 (in Japanese).