The multiplayer generalizations of Frackiewicz and Li-Du-Massar quantum schemes

Abstract

Abstract Drawing inspiration from the Frackiewicz and Li-Du-Massar quantum schemes, we provide some multiplayer generalizations of their techniques. Initially, we introduce a multiplayer version of the Frackiewicz quantum scheme, and give quantum Cournot oligopoly games with both three and n players. Our findings indicate that quantum equilibrium profits decrease monotonically with increasing entanglement levels of environments participated by oneself, but increase monotonically with the entanglement levels of other players. Subsequently, we present a multiplayer extension of the Li-Du-Massar quantum scheme, and analyze quantum Cournot oligopoly games with three and n players. We observe that quantum equilibrium profit exhibits a positive correlation with entanglement levels. Furthermore, the quantum equilibrium quantity and profit exhibit a negative correlation with the number of players for both multiplayer quantum schemes.