The Sequential Hotelling Game with One Parameterized Location

Abstract

This article studies the location–price Hotelling game. Numerous studies have been conducted on the Hotelling game with simultaneous decisions; however, in real-life scenarios, decisions are frequently sequential. Unfortunately, studies on the sequential Hotelling (SHOT) game are quite scarce. This article contributes to the study of the SHOT game by considering the case in which the location of one of the players, either the leader or the follower, is externally fixed. The game is studied analytically and by numerical simulation to address scenarios where mathematical analysis is cumbersome due to the discontinuous nature of the game. Simulation is found to be particularly useful in evaluating the subgame perfect equilibrium (SPE) solution of these SHOT games, where the follower outperforms the leader as a very general rule, with very few exceptions. This article complements a previous study of the SHOT game where the two locations are parameterized and paves the way to address the analysis of more sophisticated formulations of the SHOT game, such as those with reservation cost and with elastic demand.

Keywords

• game theory
• simulation
• Hotelling
• sequential
• equilibrium