Iterated Weaker-than-Weak Dominance

• Main Authors: CHENG, Shih-Fen, WELLMAN, Michael P.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2007
• Subjects: Artificial Intelligence and Robotics; Operations Research, Systems Engineering and Industrial Engineering
• Online Access: https://ink.library.smu.edu.sg/sis_research/840; https://ink.library.smu.edu.sg/context/sis_research/article/1839/viewcontent/IJCAI_ChengS1471.pdf
• Institution: Singapore Management University

We introduce a weakening of standard gametheoretic δ-dominance conditions, called dominance, which enables more aggressive pruning of candidate strategies at the cost of solution accuracy. Equilibria of a game obtained by eliminating a δ-dominated strategy are guaranteed to be approximate equilibria of the original game, with degree of approximation bounded by the dominance parameter. We can apply elimination of δ-dominated strategies iteratively, but the for which a strategy may be eliminated depends on prior eliminations. We discuss implications of this order independence, and propose greedy heuristics for determining a sequence of eliminations to reduce the game as far as possible while keeping down costs. A case study analysis of an empirical 2-player game serves to illustrate the technique, and demonstrate the utility of weaker-than-weak dominance pruning.