Geoscience Reference
In-Depth Information
14.2
Elements of Competitive Location Models
The subject of competitive location models, as pioneered by Hotelling, has become
a rich research area. Since research has moved into many different directions, it
is useful to classify models, e.g., by using the taxonomy proposed by Eiselt et al.
( 1993 ). Rather than describe it in detail, we will outline its major components here.
One aspect of all location models, competitive or not, is the choice of space .In
contrast to regular, noncompetitive, location models, many authors have used much
simplified spaces in their models: starting with Hotelling's original linear market,
they have also investigated circular markets, which may appear rather contrived at
first glance, but are designed to avoid the “end-of-line effects” of bounded linear
markets.
Measures of distances are no issue when devising models in a single dimension,
but they are, as soon as models in two or more dimensions are investigated. While
some authors favor gauges in noncompetitive location models (see, e.g., Durier
and Michelot 1985 ,orPlastria 1992 ) most contributions in the literature that look
at continuous location models in the plane have used Minkowski distances, most
prominently Manhattan, Euclidean, and Chebyshev distances.
A similar situation prevails in networks. Measures of distances in trees are not
an issue, as, by definition, there is only one path between each pair of points.
However, in general networks one could, at least theoretically, use any distance that
best models reality. Assuming not only rational, but also cost-minimizing behavior,
virtually all authors in the field have chosen shortest path distances. Assuming
complete information, one could choose traffic choice models and assume that
customers take not the shortest route with respect to distances, but the shortest route
with respect to time; or that not all customers use the same route selection strategy
all the time. This would suggest itself particularly in highly congested (urban) areas.
One concept that is used extensively by authors who deal with network models is
known as node property or Hakimi property . It is based on Hakimi's work ( 1964 )
on network location properties, in which he proved that in some models, at least one
optimal solution locates all facilities at the nodes of a network.
The second component concerns the number of players and facilities that are to
be located. Traditionally, papers included duopolists who locate a single facility
each, so that the terms “firm” and “facility” (the entity to be located) were
synonymous. This is, of course, no longer the case once we include multiple firms
or multiple facilities to be located by each of the planners. Here, we will use the
game-theoretic term players for the (independently operating) firms, and “facilities”
for what they are locating. The number of facilities that one or more of the players
wish to locate may be preselected or unspecified. In the latter case, the cost or profit
function of a player includes fixed costs for opening a facility at a site.
The third component of competitive location models concerns the pricing policy.
One important feature of Hotelling's original model was that he investigated
competition in location and prices. A more general model would let players also
choose their pricing policy. In particular, we typically distinguish between a variety
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