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On Hobbes’s state of nature and game theory


  • Bertrand Crettez

    () (Université Panthéon-Assas, Paris II, CRED)


Abstract Hobbes’s state of nature is often analyzed in two-person two-action non-cooperative games. By definition, this literature only focuses on duels. Yet, if we consider general games, i.e., with more than two agents, analyzing Hobbes’s state of nature in terms of duel is not completely satisfactory, since it is a very specific interpretation of the war of all against all. Therefore, we propose a definition of the state of nature for games with an arbitrary number of players. We show that this definition coincides with the strategy profile considered as the state of nature in two-person games. Furthermore, we study what we call rational states of nature (that is, strategy profiles which are both states of nature and Nash equilibria). We show that in rational states of nature, the utility level of any agent is equal to his maximin payoff. We also show that rational states of nature always exist in inessential games. Finally, we prove the existence of states of nature in a class of (not necessarily inessential) symmetric games.

Suggested Citation

  • Bertrand Crettez, 2017. "On Hobbes’s state of nature and game theory," Theory and Decision, Springer, vol. 83(4), pages 499-511, December.
  • Handle: RePEc:kap:theord:v:83:y:2017:i:4:d:10.1007_s11238-017-9626-8
    DOI: 10.1007/s11238-017-9626-8

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    References listed on IDEAS

    1. A.M. Colman & T.W. Körner & O. Musy & T. Tazdaït, 2011. "Mutual support in games: Some properties of Berge equilibria," Post-Print hal-00716357, HAL.
    2. Benjamin Powell & Edward Stringham, 2009. "Public choice and the economic analysis of anarchy: a survey," Public Choice, Springer, vol. 140(3), pages 503-538, September.
    3. Vanderschraaf, Peter, 2006. "War Or Peace?: A Dynamical Analysis Of Anarchy," Economics and Philosophy, Cambridge University Press, vol. 22(2), pages 243-279, July.
    4. Courtois, Pierre & Nessah, Rabia & Tazdaït, Tarik, 2015. "How To Play Games? Nash Versus Berge Behaviour Rules," Economics and Philosophy, Cambridge University Press, vol. 31(1), pages 123-139, March.
    5. Michael Carter, 2001. "Foundations of Mathematical Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531925, August.
    6. Michael Carter, 2001. "Foundations of Mathematical Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262032899, August.
    7. Jason Briggeman, 2009. "Governance as a strategy in state-of-nature games," Public Choice, Springer, vol. 141(3), pages 481-491, December.
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    More about this item


    State of nature; Hobbes; Nash equilibrium; Inessential games;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D02 - Microeconomics - - General - - - Institutions: Design, Formation, Operations, and Impact
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • P48 - Economic Systems - - Other Economic Systems - - - Political Economy; Legal Institutions; Property Rights; Natural Resources; Energy; Environment; Regional Studies


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