Quantum oligopoly

¹ Department of Physics, The Chinese University of Hong Kong Shatin, New Territories, Hong Kong
² Department of Natural Sciences, National Institute of Education Nanyang Technological University - 1 Nanyang Walk, Singapore 637616

Corresponding authors: cflo@phy.cuhk.edu.hk dkiang@nie.edu.sg

Received: 13 May 2003
Accepted: 6 October 2003

Abstract

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 ), 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 in both the Cournot and Bertrand oligopoly.