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Quantum Bertrand duopoly with differentiated products. (English) Zbl 1118.81401
Summary: We apply Hui Li et al.’s “minimal” quantization rules [Phys. Lett., A 306, No. 2-3, 73–78 (2002; Zbl 1005.81011)] to investigate the quantum version of the Bertrand duopoly with differentiated products. In particular, we have examined how the quantum entanglement affects the outcome of the classical game. It is found that while negative entanglement diminishes the profit of each firm below the classical limit, positive entanglement enhances the profit monotonically, reaching a maximum in the limit of maximal entanglement. As a consequence, the frustrating dilemma-like situation is completely resolved in the quantum version of the game.

MSC:
81P15 Quantum measurement theory, state operations, state preparations
91A10 Noncooperative games
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