The East End, the West End, and King's Cross: On Clustering in the Four-Player Hotelling Game

Abstract

We study experimentally a standard four-player Hotelling game, with a uniform density of consumers and inelastic demand. The pure strategy Nash equilibrium configuration consists of two firms located at one quarter of the linear city, and the other two at three quarters. We do not observe convergence to such an equilibrium. In our experimental data we find three clusters. Besides the direct proximity of the two equilibrium locations this concerns the focal mid-point. Moreover, we observe that whereas this mid-point appears to become more notable over time, other focal points fade away. We explain how these observations are related to best-response dynamics, and to the fact that the players rely on best-responses in particular when they are close to the equilibrium configuration.