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Unformatted text preview: ngly, winnerdetermination remains
NPhard even in this very restricted problem by reduction from weighted set packing.
Lehmann et al. allows the payment rules to change from those in a Groves scheme, and
propose a set of su cient axioms for strategyproofness in their problem. The axioms
apply to properties of the allocation rule and the payment rule. The most important
condition for strategyproofness is the critical" condition, which states that an agent's
payment must be independent of its bid and minimal", closely following the intuition
behind the incentivecompatibility of the VickreyClarkeGroves scheme. Lehmann et al.
propose a greedy allocation rule and a payment scheme that satis es their axioms, which
together comprise a strategyproof mechanism. Extending to doubleminded" agents, the
authors prove that there are no strategyproof payment rules compatible with their greedy
allocation method.
Nisan & Ronen NR01 present an interesting algorithmic study of mechanism design
for a task allocation problem, with a non e ciencymaximizing objective and therefore
outside of the application of Groves mechanisms. The objective in the task allocation
problem is to allocate tasks to minimize the makespan, i.e. the time to complete the nal
task. Individually, each agent wants to minimize the time that it spends performing tasks.
Nisan & Ronen present su cient conditions for the strategyproofness of a mechanism,
and consider the class of approximation algorithms that satisfy those conditions. The
69 important axioms are independence, i.e. the payment to agent i does not depend on its
own bid, and maximization, i.e. the mechanism must compute an outcome that maximizes
the bene t when each agent reports its true ability to perform tasks. For a particular class
of constantfactor approximation algorithms, the authors compute a lowerbound on the
degreeofapproximation for which strategyproofness is possible. Nisan & Ronen continue
to show that a randomized mechanism can improve this bestcase approximation factor. Distributed Methods
Nisan & Ronen NR00 propose an innovative second chance" mechanism, which aims
to combine distributed challenges by agents with an approximate winnerdetermination
algorithm. The secondchance mechanism builds on the intuition that agents will manipulate an Groves mechanism built around an approximation algorithm if they can improve
the solution by misrepresenting their own preferences, given the announcements of other
agents.
The secondchance mechanism provides a method to allow agents to improve the outcome of the algorithm without also running the risk that agents will make the solution
worse, for example if they make bad predictions about the algorithm or about the an^
nouncements from other agents. Agents submit a claim i about their preferences, as
in the standard Groves mechanism, and also an appeal function, which can be viewed
as an additional heuristic algorithm for the winnerdetermination problem. The appeal
function provides an alternative se...
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 Fall '13
 DavidParkes

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