polytope

Definition

A finite region of $n$-dimensional space enclosed by a finite number of hyperplanes.

Notes

intuitively: the $n$-dimensional generalization of polyhedra (3-dimensional) or polygons (2-dimensional)

4-dimensional polytope is known as a polychoron.

Efficient algorithms exist for finding the extreme points of a polytope, e.g. the simplex algorithm. This makes it relatively easy to compute correlated equilibria in contrast to Nash equilibria, which are computationally hard.

See also

• simplex

References

1. https://mathworld.wolfram.com/Polytope.html
2. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, pp. 308-309.
   • see remark 8.2