2002/08/28 by F. M. C. Witte, Witte, F. M. C.
Decision Sciences · Physics and Astronomy · #Decision-Making and Behavioral Economics #FOS: Physical sciences #Game Theory and Applications #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0208171
final version, 13 pages, LaTeX
arxiv created 2002/08/28 · openalex publication_date 2002/08/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent years methods have been proposed to extend classical game theory into the quantum domain. This paper explores further extensions of these ideas that may have a substantial potential for further research. Upon reformulating quantum game theory as a theory of classical games played by "quantum players" I take a constructive approach. The roles of the players and the arbiter are investigated for clues on the nature of the quantum game space. Upon examination of the role of the arbiter, a possible non-commutative nature of pay-off operators can be deduced. I investigate a sub-class of games in which the pay-off operators satisfy non-trivial commutation relations. Non-abelian pay-off operators can be used to generate whole families of quantum games.