Simulation of the quantum Bertrand–Edgeworth game

In the Bertrand–Edgeworth duopoly game, two players compete in price to capture the market demand of a uniform product. The game is studied from a general perspective, so that players with different production costs and capacity constraints as well as the two more important rules dealing with unsatisfied demand (proportional and efficient) are taken into consideration. A quantization scheme is applied to the game with the aim of improving the results compared to the classic game. The quantum Bertrand–Edgeworth duopoly game is studied in this work via spatial numerical simulation, supporting the results analytically when it is possible. In this context, it is found that high entanglement induces a Pareto optimal solution ruled by the lower capacity of the players. The way in which the players’ entanglement acts in the game is examined through simulation, paying special attention to the critical value of entanglement from which the Pareto optimal solution emerges.