274 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
Equilibrium in Labor Markets with Few Firms
We study competition between firms in labor markets, following a
combinatorial model suggested by Kelso and Crawford [1982]. In this model, each
firm is trying to recruit workers by offering a higher salary than its
competitors, and its production function defines the utility generated from any
actual set of recruited workers. We define two natural classes of production
functions for firms, where the first one is based on additive capacities
(weights), and the second on the influence of workers in a social network. We
then analyze the existence of pure subgame perfect equilibrium (PSPE) in the
labor market and its properties. While neither class holds the gross
substitutes condition, we show that in both classes the existence of PSPE is
guaranteed under certain restrictions, and in particular when there are only
two competing firms. As a corollary, there exists a Walrasian equilibrium in a
corresponding combinatorial auction, where bidders' valuation functions belong
to these classes.
While a PSPE may not exist when there are more than two firms, we perform an
empirical study of equilibrium outcomes for the case of weight-based games with
three firms, which extend our analytical results. We then show that stability
can in some cases be extended to coalitional stability, and study the
distribution of profit between firms and their workers in weight-based games
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