On acyclicity of games with cycles

Authors:
Daniel Andersson;Vladimir Gurvich;Thomas Dueholm Hansen
Affiliations:
Department of Computer Science, Aarhus University, DK-8200, Denmark;RUTCOR, Rutgers the State University of New Jersey, United States;Department of Computer Science, Aarhus University, DK-8200, Denmark
Venue:
Discrete Applied Mathematics
Year:
2010

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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.