A comment on the generalization of the Marinatto-Weber quantum game scheme

TL;DR

This paper critiques a previous generalization of the Marinatto-Weber quantum game scheme, highlighting its flaws and proposing a more robust protocol for finite bimatrix games to ensure accurate quantum game analysis.

Contribution

The paper identifies issues in Iqbal and Toor's generalization and introduces a fault-free protocol for any finite bimatrix game within the MW quantum scheme.

Findings

Identified undesirable properties in Iqbal and Toor's generalization.

Constructed a fault-free protocol for finite bimatrix games.

Enhanced the reliability of quantum game analysis.

Abstract

Iqbal and Toor [Phys. Rev. A {\bf 65}, 022306 (2002)] and [Commun. Theor. Phys. {\bf 42}, 335 (2004)] generalized the Marinatto-Weber quantum scheme for $2 \times 2$ games in order to study bimatrix games of $3 \times 3$ dimension, in particular the Rock-Paper-Scissors game. In our paper we show that Iqbal and Toor's generalization exhibits certain undesirable property that can considerably influence the game result. To support our argumentation, in the further part of the paper we construct the protocol corresponding to the MW concept for any finite bimatrix game that is free from the fault.