101 research outputs found
Mechanism Design with Strategic Mediators
We consider the problem of designing mechanisms that interact with strategic
agents through strategic intermediaries (or mediators), and investigate the
cost to society due to the mediators' strategic behavior. Selfish agents with
private information are each associated with exactly one strategic mediator,
and can interact with the mechanism exclusively through that mediator. Each
mediator aims to optimize the combined utility of his agents, while the
mechanism aims to optimize the combined utility of all agents. We focus on the
problem of facility location on a metric induced by a publicly known tree. With
non-strategic mediators, there is a dominant strategy mechanism that is
optimal. We show that when both agents and mediators act strategically, there
is no dominant strategy mechanism that achieves any approximation. We, thus,
slightly relax the incentive constraints, and define the notion of a two-sided
incentive compatible mechanism. We show that the -competitive deterministic
mechanism suggested by Procaccia and Tennenholtz (2013) and Dekel et al. (2010)
for lines extends naturally to trees, and is still -competitive as well as
two-sided incentive compatible. This is essentially the best possible. We then
show that by allowing randomization one can construct a -competitive
randomized mechanism that is two-sided incentive compatible, and this is also
essentially tight. This result also closes a gap left in the work of Procaccia
and Tennenholtz (2013) and Lu et al. (2009) for the simpler problem of
designing strategy-proof mechanisms for weighted agents with no mediators on a
line, while extending to the more general model of trees. We also investigate a
further generalization of the above setting where there are multiple levels of
mediators.Comment: 46 pages, 1 figure, an extended abstract of this work appeared in
ITCS 201
Networks of Complements
We consider a network of sellers, each selling a single product, where the
graph structure represents pair-wise complementarities between products. We
study how the network structure affects revenue and social welfare of
equilibria of the pricing game between the sellers. We prove positive and
negative results, both of "Price of Anarchy" and of "Price of Stability" type,
for special families of graphs (paths, cycles) as well as more general ones
(trees, graphs). We describe best-reply dynamics that converge to non-trivial
equilibrium in several families of graphs, and we use these dynamics to prove
the existence of approximately-efficient equilibria.Comment: An extended abstract will appear in ICALP 201
Price Competition in Online Combinatorial Markets
We consider a single buyer with a combinatorial preference that would like to
purchase related products and services from different vendors, where each
vendor supplies exactly one product. We study the general case where subsets of
products can be substitutes as well as complementary and analyze the game that
is induced on the vendors, where a vendor's strategy is the price that he asks
for his product. This model generalizes both Bertrand competition (where
vendors are perfect substitutes) and Nash bargaining (where they are perfect
complements), and captures a wide variety of scenarios that can appear in
complex crowd sourcing or in automatic pricing of related products.
We study the equilibria of such games and show that a pure efficient
equilibrium always exists. In the case of submodular buyer preferences we fully
characterize the set of pure Nash equilibria, essentially showing uniqueness.
For the even more restricted "substitutes" buyer preferences we also prove
uniqueness over {\em mixed} equilibria. Finally we begin the exploration of
natural generalizations of our setting such as when services have costs, when
there are multiple buyers or uncertainty about the the buyer's valuation, and
when a single vendor supplies multiple products.Comment: accept to WWW'14 (23rd International World Wide Web Conference
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