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

Hotelling revisits the lab: equilibration in continuous and discrete time

“…(2) a deviation to ½0; 0:25Þ or to ð0:75; 1 clearly shrinks the deviator's territory and payoff, while by (1) a deviation to ð0:25; 0:75Þ shifts the deviator's territory but does not increase payoff. For a formal proof, see appendix B of Huck et al (2002), and for a proof of the uniqueness of pure NE, see Eaton and Lipsey (1975).…”

“…In previous laboratory examinations of the Hotelling location-only game (Collins and Sherstyuk 2000;Huck et al 2002), subjects were given random initial positions and allowed to select new actions simultaneously in discrete time, i.e., in a finitely repeated game. Although the stage game is symmetric and constant sum (the total payoff is always 1.0), the players face considerable strategic uncertainty-to chose well, they must accurately predict their opponents' next location choices.…”

“…In work most closely related to this paper, Huck et al (2002) investigate the fourplayer implementation of the location-only model. Eaton and Lipsey show that all Nash equilibria are in pure strategies with two players located back-to-back at the first quartile, and the remaining two players similarly located at the third quartile.…”

The Principle of Minimum Differentiation revisited: Return of the median voter

“…We report 6 The minor differences are illustrated e.g. in Huck, Müller, and Vriend (2002), where we see that with n = 4 in equilibrium the paired players may stay either in the same location or in two neighboring ones. And of course, as noted already, in a continuous strategy space there is an infinite number of Nash equilibria for any n > 5, and thus any discretization will be able to relate to only a subset of these.…”

“…Experimental evidence for Hotelling's location game in the laboratory with n = 3 (Collins and Sherstyuk, 2000) and n = 4 (Huck, Müller, and Vriend, 2002) suggests that one may expect many non-equilibrium outcomes in this game, with in particular more choices near the center than predicted by the theory.…”