DIMACS TR: 2009-09
On acyclicity of games with cycles
Authors: Daniel Anderson, Vladimir Gurvich and Thomas Dueholm Hansen
We study restricted improvement cycles (ri-cycles) in nite positional n-person games with perfect information modeled by directed graphs (digraphs) that may contain directed cycles (di-cycles). We obtain criteria of restricted improvement acyclicity (ri-acyclicity) in two cases: for n = 2 and for acyclic digraphs. We also 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.
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