O'Neill's Theorem for Games

• 成果类型: Article; Early Access
• 署名作者: Govindan, Srihari; Laraki, Rida; Pahl, Lucas
• 署名单位: University of Rochester; Mohammed VI Polytechnic University; University of Sheffield
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0304
• 发表日期: 2025
• 关键词: form games; points

摘要

We present the following analog of O'Neill's theorem (O'Neill B (1953) Essential sets and fixed points. Amer. J. Math. 75(3):497-509 (theorem 5.2)) for finite games. Let C-1, . . . , C-k be the components of Nash equilibria of a finite normal-form game G. For each i, let c(i) be the index of C-i. For each epsilon > 0, there exist pairwise disjoint neighborhoods V-1, . . . , V-k of the components such that for any choice of finitely many distinct completely mixed strategy profiles {sigma(ij)}(ij),sigma(ij) is an element of V-i for each i = 1, . . . , k and numbers r(ij) is an element of {-1, 1} such that Sigma(j)r(ij) = c(i), there exists a normal-form game (G) over bar obtained from G by adding duplicate strategies and an epsilon-perturbation (G) over bar(epsilon) of (G) over bar such that the set of equilibria of (G) over bar(epsilon) is {(sigma) over bar(ij)}(ij), where for each i, j, (1) (sigma) over bar(ij) is equivalent to the profile sigma(ij) and (2) the index (sigma) over bar(ij) equals r(ij).