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which depends on the service time and flow cost. This model allows O/D paths
to contain more than one hub arc or to have direct connections between origins
and destinations. Luer-Villagra and Marianov (
2013
) study a competitive model in
which an existing firm uses a hub network and charges its flow costs plus a fixed
additional percentage to their customers. A new company wants to enter into the
same market using an incomplete hub network and to determine prices so as to
maximize its profit, rather than its market share. The profit comes from the revenues
from captured flows, minus the a fixed and variable costs. Customer preferences on
selected firm and route are modeled using a logit model.
Using a game theoretic framework, Sasaki and Fukushima (
2001
) introduce a
continuous Stackelberg hub location model where a large company competes with
several medium-size companies to maximize its profit. The large company first
locates a new hub on a plane as a leader, and the other companies then locate
their new hubs. The authors use a nonlinear logit function to model the level of
captured customers and formulate the leader's problem as a bilevel program and the
follower's problems as lower level programs. Sasaki (
2005
) provides an extension
to the discrete case assuming there is a leader and only one follower. The proposed
model considers that companies cannot provide any service whose captured market
share does not reach to a threshold lower limit value. Sasaki et al. (
2009
) study a
more general model in which the full interconnection assumption is relaxed and a set
of hub arcs must be located. As in Sasaki (
2005
), two firms compete for customers
in a Stackelberg framework, where the leader firm locates hub arcs to maximize
its market share, knowing that the follower will later locate its own hub arcs to
maximize its market share.
Instead of considering a pure competitive environment, some studies have looked
at hub network alliances and mergers, as well as user cooperation employing a
game theoretic approach. In Skorin-Kapov (
1998
) a cooperative game theory is used
to analyze several cost allocation problems referred to as hub network games. In
particular, the flow routing cost is distributed among the hub network users with
possibly conflicting interests, but their cooperation is essential for the exploitation
of economies of scale on the routing of flows. Lin and Lee (
2010
) propose a non-
cooperative game theoretic model to study the competition hub network design
in an oligopolistic market with few dominant firms. In this model, each firm will
first observe the hub network and demand flows of other firms and will then
simultaneously determine its hub network, demand, and routing plan in order to
maximize its profits. The firms' decisions jointly determine the market prices, which
include the reassessment and redesign of hub networks of all other firms. The
process of observation, design and reassessment will continue until a long-term
Cournot-Nash equilibrium is established.
Adler and Smilowitz (
2007
) present hub location models to analyze global
alliances and mergers in the airline industry under competition. In particular, the
authors develop a game theoretic approach in which merger and hub location
decisions are considered to evaluate hub networks under competition. The proposed
problems are modeled as games played among multiple airlines, consisting of
selecting the optimal hubs to develop, expand or remove in the newly merged hub
