Simulation of the Hotelling–Smithies game: Hotelling was not so wrong

Abstract

This work studies the Hotelling game with elastic demand, that is, the Hotelling–Smithies game, through numerical simulation. The implemented simulation technique allows to monitor the correctness of the analytical solution of the game when it is available, for example, the monopolistic model, and to explore scenarios where the analytical solution is not available or cumbersome to find. This is even the case for Nash equilibrium in games with fixed locations. In games with variable location and price, and in games with variable location and fixed price, the locations reached through the simulation drift towards the center, as stated by H. Hotelling in his seminal article.