Title: Strong isomorphism in Marinatto-Weber type quantum games,
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.