Abstract
We study two-player one-dimensional discrete Hotelling pure location games assuming that demand f(d) as a function of distance d is constant or strictly decreasing. We show that this game admits a best-response potential. This result holds in particular for f(d) = wd with 0 < w ≤ 1. For this case special attention will be given to the structure of the equilibrium set and a conjecture about the increasingness of best-response correspondences will be made.
Highlights
In his seminal paper [6], Hotelling presents a location model of two competing retailers
Our main result is that the discrete Hotelling game (dHg) is always a best-response potential game, a stronger result compared to cHg
Denote its player set by N := {1, . . . , n}, the strategy set of player i by Xi and his payoff function by ui
Summary
In his seminal paper [6], Hotelling presents a location model of two competing retailers. The more general case, allowing for elastic demand, has been thoroughly studied in [2, 17]; we further refer to this location game as the cHg (i.e., continuous Hotelling game). To our knowledge, [18] is the first article that theoretically analyses Nash equilibria of two-player discrete Hotelling games under a setting of inelastic and elastic demand by means of the demand function f (d) = wd where 0 < w ≤ 1; so inelastic demand if w = 1 and elastic demand if w = 1. The present article is concerned with two active areas of research in game theory: location games and games having a (pure) Nash equilibrium The former already has wide range of applications, and the latter is being studied in more general frameworks, location games are one of major areas in which one still does not have general results on the existence of equilibria.
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