Tesis Magíster
Equilibrium characterization for resource allocation games on single-path serial networks
Equilibrium characterizatión for resource allocatión games on single-path serial networks
Autor
Vargas Olguin, Ignacio Javier
Institución
Resumen
The Resource Allocation Game we examined in this work is a strategic interaction
where a principal distribute an infinitely divisible good among different agents based
on their specific valuations of said good. The distribution is done by a particular
scheme first studied by Kelly (1997) with no price-discrimination. In a further study
by Johari and Tsitsiklis (2004), they aim to distribute the link capacities of a network
among different users. The authors prove existence of a unique Nash equilibrium
(NE) for the base case of a single link, but for a general network only existence is
proven, leaving open questions about uniqueness. In this study we characterize the
NE for a distinct structure of networks, the single-path serial network.
The problem is tackled gradually. First, we give explicit solutions for the case
with n players with affine utility functions on a single arc. Next for networks with
different arc capacities and all players interested in the same path within the network,
uniqueness of the NE is proved. Moreover the NE is characterized by a variational
inequality that correspond to the first-order conditions of an optimization problem.
Thereupon, for the case where players might have different origin-destination pairs
without arcs in common, uniqueness of the NE in terms of flow is again proved.
Last but not least, we propose a sequential extension of the scheme. In this
framework, players do not act simultaneously, but in a given order of precedence. For
the base case of one arc and two players with linear utilities, we obtained an explicit
Subgame Perfect Equilibrium. In addition, we get a price of anarchy better than the
one obtained for the simultaneous case.
We propose some thoughts about the Transportation analysis application of this
type of networks for liner shipping and highways, that is to say situations where there
is a single-path of interest for every player. PFCHA-Becas PFCHA-Becas