Cellular automaton simulation of the quantum Hotelling game with reservation cost

This work studies the quantum Hotelling game via spatial numerical simulation. It is concluded that entanglement enables the emergence of the Pareto optimal solution in Nash equilibrium in simulations of the game with variable prices and fixed location of the players. In the rather complicated scenario of variable prices and locations, the implemented simulation technique shows that the players share the market, both locating close to ( L /4, 3 L /4). The Hotelling game is studied with both linear and quadratic transportation cost, with no relevant discrepancies found in both scenarios.