Quantum oligopoly

Based upon a modification of Li et al. 's “minimal” quantization rules (Phys. Lett. A306(2002) 73), we investigate the quantum version of the Cournot and Bertrand oligopoly. In the Cournot oligopoly, the profit of each of the N firms at the Nash equilibrium point rises monotonically with the measure of the quantum entanglement. Only at maximal entanglement, however, does the Nash equilibrium point coincide with the Pareto optimal point. In the Bertrand case, the Bertrand Paradox remains for finite entanglement (i.e., the perfectly competitive stage is reached for any $N\geqslant 2$), whereas with maximal entanglement each of the N firms will still have a non-zero shared profit. Hence, the Bertrand Paradox is completely resolved. Furthermore, a perfectly competitive market is reached asymptotically for $N\rightarrow\infty$ in both the Cournot and Bertrand oligopoly.