A Dynamic Game with Interaction Between Kantian Players and Nashian Players

  • Ngo Van LongEmail author
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 280)


This paper defines the concept of feedback Kant-Nash equilibrium for a discrete-time model of resource exploitation by infinitely-lived Kantian and Nashian players, where we define Kantian agents as those who act in accordance with the categorical imperative. We revisit a well-known dynamic model of the tragedy of the commons and ask what would happen if not all agents are solely motivated by self interest. We establish that even without external punishment of violation of social norms, if a sufficiently large fraction of the population consists of Kantian agents, the tragedy of the commons can be substantially mitigated.


Kantian equilibrium Rule of behavior Categorical imperative 


  1. Arrow, K. J. (1973). Social responsibility and economic efficiency. Public Policy, 21, 303–317.Google Scholar
  2. Breton, M., Sbragia, L., & Zaccour, G. (2010). A dynamic model of international environmental agreements. Environmental and Resource Economics, 45, 25–48.CrossRefGoogle Scholar
  3. Clément, E., Demonque, C., Hansen-Love, L., & Kahn, P. (2000). La Philosophie de A à Z. Paris: Hatier.Google Scholar
  4. Gordon, S. (1954). The economic theory of a common property resource: The fishery. Journal of Political Economy, 62(2), 124–142.CrossRefGoogle Scholar
  5. Grafton, R. Q., Kompas, T., & Long, N. V. (2017). A brave new world? Kantian-Nashian interactions and the dynamics of global climate change mitigation. European Economic Review, 99, 31–42.CrossRefGoogle Scholar
  6. Hardin, G. (1968). The tragedy of the commons. Science, 162, 1243–1248.CrossRefGoogle Scholar
  7. Harsanyi, J. (1980). Rule utilitarianism, rights, obligations, and the theory of rational behavior. Theory and Decision, 12(2), 115–133.CrossRefGoogle Scholar
  8. Hill, T. E. Jr., & Zweig, A. (2002). Groundwork for the metaphysics of morals. Oxford: Oxford University Press.Google Scholar
  9. Johnson, R., & Cureton, A. (2018). Kant’s moral philosophy. In The Stanford encyclopedia of philosophy. Palo Alto: Stanford University Press.Google Scholar
  10. Kant, I. (1785). Grundlegung zur Metaphysik der Sitten. Translated by Mary J. Gregor. (1998). Groundwork of the metaphysics of morals. Cambridge: Cambridge University Press.Google Scholar
  11. Kant, I. (1795). Zum ewigen Frieden. Ein philosophischer Entwurf. Perpetual peace: A philosophical sketch. Downloaded from Accessed 20 December 2018.
  12. Laffont, J.-J. (1975). Macroeconomic constraints, economic efficiency and ethics: An introduction to Kantian economics. Economica, 42, 430–437.CrossRefGoogle Scholar
  13. Levhari, D., & Mirman, L. (1980). The great fish wars: An example of using a dynamic Nash-Cournot solution. Bell Journal of Economics, 11, 322–334.CrossRefGoogle Scholar
  14. Long, N. V. (2016). Kant-Nash equilibrium in a quantity-setting oligopoly. In P. von Mouche & F. Quartieri (Eds.), Equilibrium theory for Cournot oligopolies and related games: Essays in honour of Koji Okuguchi (pp. 179–202). New York: Springer.CrossRefGoogle Scholar
  15. Long, N. V. (2017). Mixed-strategy Kant-Nash equilibrium in games of voluntary contributions to a public good. In W. Buchholz & D. Ruebbelke (Eds.), The theory of externalities and public goods (pp. 107–126). New York, Springer.CrossRefGoogle Scholar
  16. Long, N. V. (2018). Warm glow and the transmission of pro-socialness across generations. Journal of Public Economic Theory (in press).
  17. Muller, J. Z. (1993). Adam Smith in his time and ours: Designing the decent society. New York: The Free Press.Google Scholar
  18. Ostrom, E. (1990). Governing the commons: The evolution of institutions for collective actions. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  19. Roemer, J. E. (2010). Kantian equilibrium. Scandinavian Journal of Economics, 112(1), 1–24.CrossRefGoogle Scholar
  20. Roemer, J. E. (2015). Kantian optimization: A microfoundation for cooperation. Journal of Public Economics, 127, 45–57.CrossRefGoogle Scholar
  21. Russell, B. (1945). A history of western philosophy. London: George Allen and Unwin.Google Scholar
  22. Sen, A. (1977). Rational fools: A critique of the behavioral foundation of utility. Philosophy and Public Affairs, 6(4), 317–344.Google Scholar
  23. Sethi, R., & Somanathan, E. (1996). The evolution of social norms in common property resource use. American Economic Review, 86(4), 766–788.Google Scholar
  24. Smith, A. (1790 [2002]). The Theory of Moral Sentiments (revised edition, 1790). Edinburg: T. Creech and J. Bell & Co. Republished in the series Cambridge Texts in the History of Philosophy, edited by Knud Haakonssen, Cambridge University Press, 2002.Google Scholar
  25. Smith, V. L. (2003). Constructivist and ecological rationality in economics. American Economic Review, 93(3), 456–508.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.McGill UniversityMontréalCanada

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