Rational Generating Functions and Integer Programming Games
Skip to main content
eScholarship
Open Access Publications from the University of California

Rational Generating Functions and Integer Programming Games

  • Author(s): Köppe, Matthias
  • Ryan, Christopher Thomas
  • Queyranne, Maurice
  • et al.

Published Web Location

https://arxiv.org/pdf/0809.0689.pdf
No data is associated with this publication.
Abstract

We explore the computational complexity of computing pure Nash equilibria for a new class of strategic games called integer programming games with difference of piecewise linear convex payoffs. Integer programming games are games where players' action sets are integer points inside of polytopes. Using recent results from the study of short rational generating functions for encoding sets of integer points pioneered by Alexander Barvinok, we present efficient algorithms for enumerating all pure Nash equilibria, and other computations of interest, such as the pure price of anarchy, and pure threat point, when the dimension and number of "convex" linear pieces in the payoff functions are fixed. Sequential games where a leader is followed by competing followers (a Stackelberg--Nash setting) are also considered.

Item not freely available? Link broken?
Report a problem accessing this item