Abstract
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.
The full version of this paper with complete proofs is available as the research report, [1]. This research was supported by the Center for Algorithmic Game Theory at Aarhus University, funded by the Carlsberg Foundation. The second author was partially supported also by DIMACS, Center for Discrete Mathematics and Theoretical Computer Science, Rutgers University, and by Graduate School of Information Science and Technology, University of Tokyo.
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Andersson, D., Gurvich, V., Hansen, T.D. (2009). On Acyclicity of Games with Cycles. In: Goldberg, A.V., Zhou, Y. (eds) Algorithmic Aspects in Information and Management. AAIM 2009. Lecture Notes in Computer Science, vol 5564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02158-9_4
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DOI: https://doi.org/10.1007/978-3-642-02158-9_4
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