Optimal Pricing Policies for Public Transportation Netwo&

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真正数学味口的一篇paper，而且上了SIAM的首页期刊推荐，不太明白啊！

2006 Society for Industrial and Applied Mathematics
SIAM J. OPTIM. Vol. 16, No. 3, pp. 826–853
OPTIMAL PRICING POLICIES FOR PUBLIC TRANSPORTATION NETWORKS
GIUSEPPE BUTTAZZO†, ALDO PRATELLI‡, AND EUGENE STEPANOV†
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 Σ ⊂ Rn of finite length, the densities of the population and of the services(or workplaces), modeled by the respective finite Borel measures ϕ0 and ϕ1, and 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 it 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.
Key words. optimal transportation, transportation network, Monge–Kantorovich problem,optimal pricing, Nash equilibrium