2006/12/16 by Ruchira S. Datta, Datta, Ruchira S.
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #13P99 #91A10 #Artificial Intelligence in Games #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Game Theory and Applications #Game Theory and Voting Systems #math.AC #math.CO #msc:13P99 #msc:91A10
paper · pdf · doi:10.48550/arxiv.math/0612463
arxiv created 2006/12/16 · openalex publication_date 2006/12/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a theorem computing the number of solutions to a system of equations which is generic subject to the sparsity conditions embodied in a graph. We apply this theorem to games obeying graphical models and to extensive-form games. We define emergent-node tree structures as additional structures which normal form games may have. We apply our theorem to games having such structures. We briefly discuss how emergent node tree structures relate to cooperative games.