Non-Transitive Quantum Games

Non-transitivity can arise in games with three or more strategies $A,B,C$, when $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$, ($A>B>C>A$). An example is the children's game \textquotedblleft rock, scissors, paper" ($R,S,P$) where $R>S>P>R$. We discuss the conditions under which quantum versions of $R,S,P$ retain the non-transitive characteristics of the corresponding classical game. Some physical implications of non-transitivity in quantum game theory are also considered.