# Dominated Actions in Imperfect-Information Games

arXiv: https://arxiv.org/abs/2504.09716 · HTML: https://mlsanity.com/paper/2504.09716/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 17 references that are in the map.
- First posted on arXiv 13 Apr 2025.

## Builds on (most cited first, 1 of 1)

- [Mistakes in Games](https://mlsanity.com/paper/1910.00225/) (2019)

## Built on by (most cited first, 2 of 2)

- [Quadratic Programming Approach for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games](https://mlsanity.com/paper/2509.25618/) (2025)
- [Variable Bound Tightening for Nash Equilibrium Computation in Multiplayer Imperfect-Information Games](https://mlsanity.com/paper/2606.25997/) (2026)

## Abstract (arXiv)

Dominance is a fundamental concept in game theory. In normal-form games dominated strategies can be identified in polynomial time. As a consequence, iterative removal of dominated strategies can be performed efficiently as a preprocessing step for reducing the size of a game before computing a Nash equilibrium. For imperfect-information games in extensive form, we could convert the game to normal form and then iteratively remove dominated strategies in the same way; however, this conversion may cause an exponential blowup in game size. In this paper we define and study the concept of dominated actions in imperfect-information games. Our main result is a polynomial-time algorithm for determining whether an action is dominated (strictly or weakly) by any mixed strategy in two-player perfect-recall games with publicly observable actions, which can be extended to iteratively remove dominated actions. This allows us to efficiently reduce the size of the game tree as a preprocessing step for Nash equilibrium computation. We explore the role of dominated actions empirically in "All In or Fold" No-Limit Texas Hold'em poker.