On acyclicity of games with cycles

被引：10

作者：

Andersson, Daniel ^{[1
]}

Gurvich, Vladimir ^{[2
]}

Hansen, Thomas Dueholm ^{[1
]}

机构：

[1] Aarhus Univ, Dept Comp Sci, DK-8200 Aarhus, Denmark

[2] Rutgers State Univ, RUTCOR, Piscataway, NJ 08855 USA

来源：

DISCRETE APPLIED MATHEMATICS | 2010年 / 158卷 / 10期

关键词：

Positional game; Game form; Improvement cycle; Restricted improvement cycle; Restricted acyclicity; Nash equilibrium; Nash-solvability; POTENTIAL GAMES;

D O I：

10.1016/j.dam.2010.02.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study restricted improvement cycles (ri-cycles) in finite positional n-person games with perfect information modeled by directed graphs (di-graphs) that may contain directed cycles (di-cycles). We assume that all these di-cycles form one outcome c, for example, a draw. We obtain criteria of restricted improvement acyclicity (ri-acyclicity) in two cases: for n = 2 and for acyclic di-graphs. We provide several examples that outline the limits of these criteria and show that, essentially, there are no other ri-acyclic cases. We also discuss connections between ri-acyclicity and some open problems related to Nash-solvability. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1049 / 1063

页数：15

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