7 research outputs found
A New Lower Bound for Deterministic Truthful Scheduling
We study the problem of truthfully scheduling tasks to selfish
unrelated machines, under the objective of makespan minimization, as was
introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the
current gap of on the approximation ratio of deterministic truthful
mechanisms is a notorious open problem in the field of algorithmic mechanism
design. We provide the first such improvement in more than a decade, since the
lower bounds of (for ) and (for ) by
Christodoulou et al. [SODA'07] and Koutsoupias and Vidali [MFCS'07],
respectively. More specifically, we show that the currently best lower bound of
can be achieved even for just machines; for we already get
the first improvement, namely ; and allowing the number of machines to
grow arbitrarily large we can get a lower bound of .Comment: 15 page
Non-Obvious Manipulability for Single-Parameter Agents and Bilateral Trade
A recent line of work in mechanism design has focused on guaranteeing
incentive compatibility for agents without contingent reasoning skills:
obviously strategyproof mechanisms guarantee that it is "obvious" for these
imperfectly rational agents to behave honestly, whereas non-obviously
manipulable (NOM) mechanisms take a more optimistic view and ensure that these
agents will only misbehave when it is "obvious" for them to do so. Technically,
obviousness requires comparing certain extrema (defined over the actions of the
other agents) of an agent's utilities for honest behaviour against dishonest
behaviour.
We present a technique for designing NOM mechanisms in settings where
monetary transfers are allowed based on cycle monotonicity, which allows us to
disentangle the specification of the mechanism's allocation from the payments.
By leveraging this framework, we completely characterise both allocation and
payment functions of NOM mechanisms for single-parameter agents. We then look
at the classical setting of bilateral trade and study whether and how much
subsidy is needed to guarantee NOM, efficiency, and individual rationality. We
prove a stark dichotomy; no finite subsidy suffices if agents look only at
best-case extremes, whereas no subsidy at all is required when agents focus on
worst-case extremes. We conclude the paper by characterising the NOM mechanisms
that require no subsidies whilst satisfying individual rationality.Comment: 18 pages, 3 figure
The Power of Verification for Greedy Mechanism Design
Greedy algorithms are known to provide, in polynomial time, near optimal approximation guarantees for Combinatorial Auctions (CAs) with multidimensional bidders. It is known that truthful greedy-like mechanisms for CAs with multi-minded bidders do not achieve good approximation guarantees.
In this work, we seek a deeper understanding of greedy mechanism design and investigate under which general assumptions, we can have efficient and truthful greedy mechanisms for CAs. Towards this goal, we use the framework of priority algorithms and weak and strong verification, where the bidders are not allowed to overbid on their winning set or on any subset of this set, respectively. We provide a complete characterization of the power of weak verification showing that it is sufficient and necessary for any greedy fixed priority algorithm to become truthful with the use of money or not, depending on the ordering of the bids. Moreover, we show that strong verification is sufficient and necessary to obtain a 2-approximate truthful mechanism with money, based on a known greedy algorithm, for the problem of submodular CAs in finite bidding domains. Our proof is based on an interesting structural analysis of the strongly connected components of the declaration graph