Nash conditional independence curve

Pub Date : 2023-08-01 DOI:10.1016/j.jsc.2023.102255

Irem Portakal , Javier Sendra–Arranz

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引用次数: 1

Abstract

We study the Spohn conditional independence (CI) variety $C_{X}$ of an n-player game X for undirected graphical models on n binary random variables consisting of one edge. For a generic game, we show that $C_{X}$ is a smooth irreducible complete intersection curve (Nash conditional independence curve) in the Segre variety ${(P^{1})}^{n - 2} \times P^{3}$ and we give an explicit formula for its degree and genus. We prove two universality theorems for $C_{X}$ : The product of any affine real algebraic variety with the real line or any affine real algebraic variety in $R^{m}$ defined by at most $m - 1$ polynomials is isomorphic to an affine open subset of $C_{X}$ for some game X.

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纳什条件独立曲线

本文研究了n人博弈X的无向图形模型的Spohn条件独立(CI)变量CX。对于一类泛型博弈，我们证明了CX是Segre变量(P1)n−2×P3上的光滑不可约完全相交曲线(纳什条件无关曲线)，并给出了它的次和属的显式公式。证明了CX的两个普适定理:Rm中由至多m - 1个多项式定义的任何仿射实代数变量与实直线的乘积或任何仿射实代数变量对某对策X同构于CX的仿射开子集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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