Abstract
The aim of the paper is to draw attention to a special class of two parameter unitary strategies in the Eisert-Wilkens-Lewenstein scheme for quantum games. We identify the players’ strategies with basis change matrices. Then we prove that the resulting quantum game is invariant with respect to isomorphic transformations of the input game. Moreover, it is shown that the game so obtained may not be trivial with respect to pure Nash equilibria, compared with the model with strategies being the special unitary group SU(2).
Highlights
The EWL scheme introduced in [1] has become commonly used quantum scheme for games in strategic form
Among the sets of unitary strategies {U (θ, α, β)}, {U (θ, α, 0)} and {U (θ, 0, β)} only the EWL scheme with the three-parameter operators is invariant with respect to strongly isomorphic transformations of input games
We prove that the EWL scheme based on (15) is invariant with respect to strong isomorphism
Summary
The EWL scheme introduced in [1] has become commonly used quantum scheme for games in strategic form. It seems unlikely that the restriction to the two-parameter set of unitary operators reflects any reasonable physical constraint [8] They are not reasonable from a game theory point of view - the EWL approach defined in this way may yield different optimal strategy profiles depending on the order of players’ strategies in the classical game. In other words, this scheme is not invariant under isomorphic transformations of the input game [9]. At the same time we find a scheme that justifies this type of unitary strategies
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
