On acyclicity of games with cycles

https://doi.org/10.1016/j.dam.2010.02.006Get rights and content
Under an Elsevier user license
open archive

Abstract

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.

Keywords

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

Cited by (0)

This research was supported by the Center for Algorithmic Game Theory at Aarhus University, funded by the Carlsberg Foundation.