Abstract: The quantum game of the classical Bertrands duopoly model was generalized to N-player case. In a quantized game, the more entanglement is involved, the higher maximal profits it will be. It monotonously increases until the optimal collusive profit, which is restricted, and cannot be achieved in its classical game. With partial information entanglement between two adjacent firms, the generalizing evolutionary N-player Bertrands model not only solved the Bertrand paradox, but also achieved a practical result.

Key words: quantum game, quantum entanglement, Bertrand model