Introduction

We consider game theoretic models of the transportation industry, which include mod-
els of vehicle use and travel and competition between transportation service providers,
additionally incorporating behavioral insights regarding passenger decisions, and focusing
on appropriate welfare measures.

We consider a market where the customers are distributed in the vertexes of a trans-
portation graph. The edges of the graph are transportation links (railways, car and air
lines, etc.). The vertexes are the hubs (bus stops, airports, railway stations, etc.). The
customers are the passengers, who use this kind of transportation. The demand is deter-
mined by the ow of passengers. There are n companies (players), who make a service
in this market. First, the players form their transportation networks, and then they an-
nounce the prices for the service. The consumers choose a service, the use of which leads
to the lowest personal costs. The objective of a player (transport company) is to maximize
the payo.

We consider utility function (for passengers) of various kinds, taking into account the
price of service, location of stops, time of service etc. Passenger trac is distributed
between competing companies in accordance with the selected utility function. Service
companies like to maximise their income.

Knowledge of equilibrium allows us to predict the stable state of a complex system, to
which it will come after a certain period of time. Two approaches will be used. To describe
the economic equilibrium, the Nash equilibrium will be used, and for the description of
the equilibrium of trac ows - the Wardrop equilibrium.

In 1952 Wardrop hypothesized that any transport system reaches an equilibrium state
after some period of time, as well as formulated two principles of equilibrium trac ows
distribution. According to the rst principle, the trip time on all existing routes is same
for all road users and smaller than the trip time of any road user in the case of its route
diversion. The second principle claimed that the average trip time gets minimized.

In many cases, Wardrop equilibria coincide with Nash equilibria as a basic solution
concept in non-cooperative game theory. Wardrop's ideas can be further developed by
assuming that not only trip time, but also the total costs of road users on all routes are
same and minimal. The cost function may include service price, the average trip time,
risks and so on.

Transportation model can be considered as a potential game. Potential games were
introduced by Monderer and Shapley. In the potential game the equilibrium construction
is equivalent to optimization problem in which we need to nd the maximum of potential
function. We demonstrate the eciency of this approach in some examples of routing and
pricing problems.

Contact Information

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