Equivalence between quantum simultaneous games and quantum sequential games

TL;DR

This paper establishes that quantum simultaneous and quantum sequential games are fundamentally equivalent, demonstrating that each type can be transformed into the other within a rigorous framework.

Contribution

It introduces a formal framework and proves the equivalence between quantum simultaneous and quantum sequential games, including finite versions.

Findings

Quantum simultaneous and sequential games are equivalent.

Finite versions of these games are also equivalent.

Theorems establish mutual convertibility between game types.

Abstract

A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are defined. In addition, a notion of equivalence between two games is defined. Finally, the following three theorems are shown: (1) For any quantum simultaneous game G, there exists a quantum sequential game equivalent to G. (2) For any finite quantum simultaneous game G, there exists a finite quantum sequential game equivalent to G. (3) For any finite quantum sequential game G, there exists a finite quantum simultaneous game equivalent to G.