Computational Mechanism Design Chapter 3

Lehmann et al allows the payment rules to change from

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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 allocation method. 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 agents. 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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