On the Hotelling Game with Close Players

Abstract

The principle of minimum differentiation stated by Hotelling in his pioneer paper was proved to be invalid 50 years later, since there is a region where the players are so close that Nash equilibrium does not exist. Some authors have contributed with amendments to the original game in the aim of ensuring the existence of Nash equilibrium independently of the location of the players. However, this work analyzes the less frequently studied case of the Hotelling game with close players under different implementations of the game, considering elastic and inelastic demand (conventional Hotelling game, the Hotelling game with reservation cost and Hotelling-Smithies game). The study is supported by means of numerical simulation of the game.