On Iterated Dominance, Matrix Elimination, and Matched Paths

TL;DR

This paper investigates the computational complexity of iterated dominance in anonymous games, revealing NP-completeness in three-action cases and exploring matrix elimination and matching problems to identify tractable instances.

Contribution

It establishes the NP-completeness of iterated weak dominance in three-action anonymous games and connects matrix elimination to graph matching problems, highlighting complexity boundaries.

Findings

Deciding iterated weak dominance in three-action anonymous games is NP-complete.

Matrix elimination complexity remains open but relates to path matching in directed graphs.

Certain classes of anonymous games allow polynomial-time solutions for iterated dominance.

Abstract

We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated weak dominance. The two-action case can be reformulated as a natural elimination problem on a matrix, the complexity of which turns out to be surprisingly difficult to characterize and ultimately remains open. We however establish connections to a matching problem along paths in a directed graph, which is computationally hard in general but can also be used to identify tractable cases of matrix elimination. We finally identify different classes of anonymous games where iterated dominance is in P and NP-complete, respectively.