A new model for quantum games based on the Marinatto-Weber approach

TL;DR

This paper critiques the traditional Marinatto-Weber quantum game approach and proposes modifications to better reflect true quantum strategic interactions by extending players' strategies.

Contribution

It introduces a modified quantum game model that addresses limitations of the original Marinatto-Weber scheme through strategy set extension.

Findings

Original scheme has limitations in reflecting quantum strategies.

Modified scheme extends strategy sets to improve quantum game representation.

Proposed model better captures quantum strategic behavior.

Abstract

The Marinatto-Weber approach to quantum game is a straightforward way to apply the power of quantum mechanics to classical game theory. In the simplest case, the quantum scheme is that players manipulate their own qubits of a two-qubit state either with the identity operator or the Pauli operator $\sigma_{x}$. However, such a simplification of the scheme raises doubt as to whether it could really reflect a quantum game. In this paper we put forward examples which may constitute arguments against the present form of the Marinatto-Weber scheme. Next, we modify the scheme to eliminate the undesirable properties of the protocol by extending the players' strategy sets.