*Published Paper*

**Inserted:** 29 jun 2004

**Last Updated:** 6 mar 2006

**Journal:** SIAM J. Opt

**Volume:** 16

**Number:** 3

**Pages:** 826-853

**Year:** 2006

**Abstract:**

In this paper we study the problem of finding an optimal
pricing policy
for the use of the public transportation network
in a given populated area. The transportation network,
modeled by a Borel set $\Sigma\subset *R*^n$ of finite length, the densities
of the population and of the services (or workplaces), modeled by the
respective finite Borel measures $\varphi_0$ and $\varphi_1$, as
well as the effective cost $A(t)$ for a citizen to cover
a distance $t$ without the use of the transportation
network, are assumed to be given. The pricing policy to be found
is then a cost $B(t)$ to cover
a distance $t$ with the use of the transportation
network (i.e.\ the ``price of the ticket for a distance $t$''), and
has to provide an equilibrium between the needs of the population
(hence minimizing the total cost of transportation of the population
to the services*workplaces) and that of the owner of the transportation
network (hence maximizing the total income of the latter). We present a model
for such a choice and discuss the existence as well as some qualitative
properties of the resulting optimal pricing policies.*

**Keywords:**
optimal transportation, transportation network, optimal pricing, Nash equilibrium

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