On Acyclicity of Games with Cycles

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 riacyclic cases. We also discuss connections between ri-acyclicity and some open problems related to Nash-solvability. Key words: Positional game, game form, improvement cycle, restricted improvement cycle, restricted acyclicity, Nash equilibrium, Nash-solvability 1 Main Concepts and Results

• Type: Conference
• Year: 2009
• Where: AAIM
• Authors: Daniel Andersson, Vladimir Gurvich, Thomas Dueholm Hansen
• Keywords: AAIM 2009, Acyclic Digraphs, Algorithms, Improvement Cycle, Positional N-person Games