---
title: "Iterated Weaker-than-Weak Dominance"
authors:
  - "Shih-Fen Cheng"
  - "Michael P. Wellman"
doi: ""
url: "https://ijcai.org/proceedings/2007/199"
pdf: "https://ijcai.org/proceedings/2007/0199.pdf"
venue: "Proceedings of the Twentieth International Joint Conference on Artificial Intelligence"
year: 2007
pages: "1233-1237"
track: ""
keywords:
---

# Iterated Weaker-than-Weak Dominance

Shih-Fen Cheng, Michael P. Wellman

*Proceedings of the Twentieth International Joint Conference on Artificial Intelligence*, pages 1233-1237.

## 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.