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Published in:
2009 | OriginalPaper | Chapter
On Acyclicity of Games with Cycles
Authors : Daniel Andersson, Vladimir Gurvich, Thomas Dueholm Hansen
Published in: Algorithmic Aspects in Information and Management
Publisher: Springer Berlin Heidelberg
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We study restricted improvement cycles (ri-cycles) in finite positional
n
-person games with perfect information modeled by directed graphs (digraphs) that may contain cycles. We obtain criteria of restricted improvement acyclicity (ri-acyclicity) in two cases: for
n
= 2 and for acyclic digraphs. 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.