Uniform Proofs of Order Independence for Various Strategy Elimination Procedures

TL;DR

This paper presents simple, uniform proofs demonstrating that various strategy elimination procedures in finite strategic games are order-independent, applicable to both pure and mixed strategies, based on structural properties and classical reduction system results.

Contribution

It introduces elementary, uniform proofs of order independence for multiple strategy elimination procedures using Newman's Lemma and reduction system theory.

Findings

Order independence holds for various elimination procedures.

Proofs are uniform and rely on structural properties.

Applicable to both pure and mixed strategies.

Abstract

We provide elementary and uniform proofs of order independence for various strategy elimination procedures for finite strategic games, both for dominance by pure and by mixed strategies. The proofs follow the same pattern and focus on the structural properties of the dominance relations. They rely on Newman's Lemma established in 1942 and related results on the abstract reduction systems.