Strong isomorphism in Marinatto-Weber type quantum games

TL;DR

This paper investigates a new criterion for quantum game schemes, focusing on strong isomorphism in Marinatto-Weber type quantum games, ensuring quantum schemes preserve classical game isomorphism and analyzing its impact on players' strategies.

Contribution

It introduces a strong isomorphism criterion for quantum game schemes, specifically in Marinatto-Weber type, linking classical and quantum game isomorphisms.

Findings

Quantum game schemes must generate classical games as special cases.

Strong isomorphism influences players' strategy sets in quantum games.

Marinatto-Weber quantum schemes can preserve classical game isomorphism under certain conditions.

Abstract

Our purpose is to focus attention on a new criterion for quantum schemes by bringing together the notions of quantum game and game isomorphism. A quantum game scheme is required to generate the classical game as a special case. Now, given a quantum game scheme and two isomorphic classical games, we additionally require the resulting quantum games to be isomorphic as well. We show how this isomorphism condition influences the players' strategy sets. We are concerned with the Marinatto-Weber type quantum game scheme and the strong isomorphism between games in strategic form.