## Hard-to-solve bimatrix games (2006)

Venue: | ECONOMETRICA |

Citations: | 23 - 1 self |

### BibTeX

@ARTICLE{Savani06hard-to-solvebimatrix,

author = {Rahul Savani and Bernhard von Stengel},

title = {Hard-to-solve bimatrix games},

journal = {ECONOMETRICA},

year = {2006},

volume = {74},

number = {2},

pages = {397--429}

}

### Years of Citing Articles

### OpenURL

### Abstract

The Lemke–Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d-space. The construction is extended to nonsquare games where, in addition to exponentially long Lemke–Howson computations, finding an equilibrium by support enumeration takes on average exponential time.