Unformatted text preview: ngly, winner-determination remains
NP-hard 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 strategy-proofness in their problem. The axioms
apply to properties of the allocation rule and the payment rule. The most important
condition for strategy-proofness 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 incentive-compatibility of the Vickrey-Clarke-Groves scheme. Lehmann et al.
propose a greedy allocation rule and a payment scheme that satis es their axioms, which
together comprise a strategy-proof mechanism. Extending to double-minded" agents, the
authors prove that there are no strategy-proof payment rules compatible with their greedy
Nisan & Ronen NR01 present an interesting algorithmic study of mechanism design
for a task allocation problem, with a non e ciency-maximizing 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 strategy-proofness 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 constant-factor approximation algorithms, the authors compute a lower-bound on the
degree-of-approximation for which strategy-proofness is possible. Nisan & Ronen continue
to show that a randomized mechanism can improve this best-case approximation factor. Distributed Methods
Nisan & Ronen NR00 propose an innovative second chance" mechanism, which aims
to combine distributed challenges by agents with an approximate winner-determination
algorithm. The second-chance 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
The second-chance 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 winner-determination problem. The appeal
function provides an alternative se...
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This document was uploaded on 03/19/2014 for the course COMP CS286r at Harvard.
- Fall '13