{"type":"ScholarlyArticle","title":"Iterated Weaker-than-Weak Dominance","authors":[{"name":"Shih-Fen Cheng","slug":"shih-fen-cheng","given":"Shih-Fen","family":"Cheng","affiliation":""},{"name":"Michael P. Wellman","slug":"michael-p-wellman","given":"Michael P.","family":"Wellman","affiliation":""}],"abstract":"We introduce a weakening of standard game-theoretic dominance conditions, called δ-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, δ. We can apply elimination of δ-dominated strategies iteratively, but the δ 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.","doi":null,"url":"https://ijcai.org/proceedings/2007/199","pdf":"https://ijcai.org/proceedings/2007/0199.pdf","markdown":"https://ijcai.org/proceedings/2007/199.md","bibtex":"https://ijcai.org/proceedings/2007/bibtex/199","volume":{"slug":"2007","title":"Proceedings of the Twentieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2007","url":"https://ijcai.org/proceedings/2007/","year":2007,"location":"Hyderabad, India","dates":"","editors":"Ramon López de Mántaras","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":199,"pages":{"first":1233,"last":1237},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}