IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v83y2017i4d10.1007_s11238-017-9626-8.html
   My bibliography  Save this article

On Hobbes’s state of nature and game theory

Author

Listed:
  • Bertrand Crettez

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

Abstract

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-017-9626-8
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:theord:v:83:y:2017:i:4:d:10.1007_s11238-017-9626-8. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: http://www.springer.com .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.