Universality of Nash Equilibria

@article{Datta2003UniversalityON,
  title={Universality of Nash Equilibria},
  author={R. Datta},
  journal={Math. Oper. Res.},
  year={2003},
  volume={28},
  pages={424-432}
}
  • R. Datta
  • Published 2003
  • Computer Science, Mathematics
  • Math. Oper. Res.
  • Every real algebraic variety is isomorphic to the set of totally mixed Nash equilibria of some three-person game, and also to the set of totally mixed Nash equilibria of anN-person game in which each player has two pure strategies. From the Nash-Tognoli Theorem it follows that every compact differentiable manifold can be encoded as the set of totally mixed Nash equilibria of some game. Moreover, there exist isolated Nash equilibria of arbitrary topological degree. 

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 23 REFERENCES
    Rational Learning Leads to Nash Equilibrium
    • 680
    • PDF
    Graphical Models for Game Theory
    • 629
    • PDF
    Computation of equilibria in finite games
    • 358
    • PDF
    Oddness of the number of equilibrium points: A new proof
    • 221
    SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS
    • 552
    • PDF
    Computing Equilibria of N-Person Games
    • 170
    • PDF
    Topology of Real Algebraic Sets
    • 126
    • PDF
    Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
    • 562
    • PDF