### Abstract

Existence and location of Nash equilibrium points are studied for a large class of a finite family of payoff functions whose domains are not necessarily convex in the usual sense. The geometric idea is to embed these non-convex domains into suitable Riemannian manifolds regaining certain geodesic convexity properties of them. By using recent non-smooth analysis on Riemannian manifolds and a variational inequality for acyclic sets, an efficient location result of Nash equilibrium points is given. Some examples show the applicability of our results.

Original language | English |
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Pages (from-to) | 1803-1810 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 138 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2010 |

### Fingerprint

### Keywords

- Nash equilibrium point
- Nonsmooth analysis
- Riemannian manifold

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Location of nash equilibria : A riemannian geometrical approach.** / Kristály, A.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 138, no. 5, pp. 1803-1810. https://doi.org/10.1090/S0002-9939-09-10145-4

}

TY - JOUR

T1 - Location of nash equilibria

T2 - A riemannian geometrical approach

AU - Kristály, A.

PY - 2010/5

Y1 - 2010/5

N2 - Existence and location of Nash equilibrium points are studied for a large class of a finite family of payoff functions whose domains are not necessarily convex in the usual sense. The geometric idea is to embed these non-convex domains into suitable Riemannian manifolds regaining certain geodesic convexity properties of them. By using recent non-smooth analysis on Riemannian manifolds and a variational inequality for acyclic sets, an efficient location result of Nash equilibrium points is given. Some examples show the applicability of our results.

AB - Existence and location of Nash equilibrium points are studied for a large class of a finite family of payoff functions whose domains are not necessarily convex in the usual sense. The geometric idea is to embed these non-convex domains into suitable Riemannian manifolds regaining certain geodesic convexity properties of them. By using recent non-smooth analysis on Riemannian manifolds and a variational inequality for acyclic sets, an efficient location result of Nash equilibrium points is given. Some examples show the applicability of our results.

KW - Nash equilibrium point

KW - Nonsmooth analysis

KW - Riemannian manifold

UR - http://www.scopus.com/inward/record.url?scp=77951172016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951172016&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-09-10145-4

DO - 10.1090/S0002-9939-09-10145-4

M3 - Article

AN - SCOPUS:77951172016

VL - 138

SP - 1803

EP - 1810

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -