Equivalence between quantum simultaneous games and quantum sequential games

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.