Rational Generating Functions and Integer Programming Games

• 成果类型: Article
• 署名作者: Koeppe, Matthias; Ryan, Christopher Thomas; Queyranne, Maurice
• 署名单位: University of California System; University of California Davis; University of Chicago; University of British Columbia
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1110.0964
• 发表日期: 2011
• 页码: 1445-1460
• 关键词: nash equilibria; algorithm; complexity

摘要

We explore the computational complexity of computing pure Nash equilibria for a new class of strategic games called integer programming games, with differences of piecewise-linear convex functions as 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.