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On the geometry of Nash equilibria and correlated equilibria


  • Robert Nau


  • Sabrina Gomez Canovas
  • Pierre Hansen


It is well known that the set of correlated equilibrium distributions of an n-player noncooperative game is a convex polytope that includes all the Nash equilibrium distributions. We demonstrate an elementary yet surprising result: the Nash equilibria all lie on the boundary of the polytope. Copyright Springer-Verlag 2004

Suggested Citation

  • Robert Nau & Sabrina Gomez Canovas & Pierre Hansen, 2004. "On the geometry of Nash equilibria and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 443-453, August.
  • Handle: RePEc:spr:jogath:v:32:y:2004:i:4:p:443-453 DOI: 10.1007/s001820300162

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    References listed on IDEAS

    1. MERTENS, Jean-François & ZAMIR, Shmuel, 1995. "Incomplete Information Games and the Normal Distribution," CORE Discussion Papers 1995020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. CALCAGNO, Riccardo & LOVO, Stefano M., 1998. "Bid-ask price competition with asymmetric information between market makers," CORE Discussion Papers 1998016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, March.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, March.
    4. Calcagno, Riccardo & Lovo, Stefano M., 1998. "Bid-Ask Price Competition with Asymmetric Information between Market Makers," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1998012, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
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    Cited by:

    1. Viossat, Yannick, 2006. "The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games," SSE/EFI Working Paper Series in Economics and Finance 641, Stockholm School of Economics.
    2. Yannick Viossat, 2010. "Properties and applications of dual reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 53-68, July.
    3. Ramsey, David M. & Szajowski, Krzysztof, 2008. "Selection of a correlated equilibrium in Markov stopping games," European Journal of Operational Research, Elsevier, vol. 184(1), pages 185-206, January.
    4. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
    5. Fook Kong & Berç Rustem, 2013. "Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity," Journal of Global Optimization, Springer, vol. 57(1), pages 251-277, September.

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