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Congestion Games with Variable Demands.

Fri, 12/10/2010 - 16:01 — SomNambul
Authors: Tobias Harks, Max Klimm
Subjects: Computer Science and Game Theory
link: http://arxiv.org/abs/1012.1938
Abstract

We initiate the study of congestion games with variable demands where the
(variable) demand has to be assigned to exactly one subset of resources. The
players' incentives to use higher demands are stimulated by non-decreasing and
concave utility functions. The payoff for a player is defined as the difference
between the utility of the demand and the associated cost on the used
resources. Although this class of non-cooperative games captures many elements
of real-world applications, it has not been studied in this generality, to our
knowledge, in the past.

We study the fundamental problem of the existence of pure Nash equilibria
(PNE for short) in congestion games with variable demands. We call a set of
cost functions C consistent if every congestion game with variable demands and
cost functions in C possesses a PNE. We say that C is FIP consistent if every
such game possesses the alpha-Finite Improvement Property for every alpha>0.
Our main results are structural characterizations of consistency and FIP
consistency for twice continuously differentiable cost functions. Specifically,
we show 1. C is consistent if and only if C contains either only affine
functions or only homogeneously exponential functions (c(x) = a exp(p x)). 2. C
is FIP consistent if and only if C contains only affine functions. Our results
provide a complete characterization of consistency of cost functions revealing
structural differences to congestion games with fixed demands (weighted
congestion games), where in the latter even inhomogeneously exponential
functions are FIP consistent.

Finally, we study consistency and FIP consistency of cost functions in a
slightly different class of games, where every player experiences the same cost
on a resource (uniform cost model). We give a characterization of consistency
and FIP consistency showing that only homogeneously exponential functions are
consistent.

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