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

• Published in: Communications in nonlinear science & numerical simulation 2022-09, Vol.112, p.106513, Article 106513
• Main Authors: Grau-Climent, Juan, Garcia-Perez, Luis, Losada, Juan C., Alonso-Sanz, Ramon
• Format: Article
• Language: English
• Subjects: Elastic demand; Equilibrium; Exact solutions; Game theory; Games; Hotelling; Inelastic demand; Mathematical models; Simulation
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2022.106513

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. •Numerical simulation is a powerful tool to study the Hotelling-Smithie (HS) game, particularly regarding its Nash equilibrium (NE)•Simulation allows to study the HS game when NE does not exist, i.e., with very close players.•With fixed locations, the NE solution is not far from the Pareto optimal solution.•The increase of the reservation cost induces NE with locations fairly close to the center.•In the HS game, the claim from H.Hotelling regarding the braked drift to the center remains valid.