Computational Mechanism Design Chapter 3

The revelation principle provides a very important

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Unformatted text preview: ossible outcomes. The revelation principle provides a very important theoretical tool, but is not useful in a constructive sense in di cult domains. The transformation assumed in the revelation principle from indirect mechanisms e.g. an iterative auction to direct-revelation mechanisms e.g. a sealed-bid auction assumes unlimited computational resources, both for agents in submitting valuation functions, and for the auctioneer in computing the outcome of a mechanism Led89 . In particular, the revelation principle assumes: | agents can compute and communicate their complete preferences | the mechanism can compute the correct outcome with complete information about all relevant decentralized information in the system. It can soon become impractical for an agent to compute and communicate its complete preferences to the mechanism, and for the mechanism to compute a solution to the centralized optimization problem. Direct-revelation mechanisms convert decentralized problems into centralized problems. Yet, the revelation principle does have a vital role in the design of all mechanisms, both direct and indirect, sealed-bid and iterative. The revelation principle provides focus 63 to the design of iterative mechanisms. Taken along with the uniqueness of the Groves mechanisms amongst all e cient and dominant-strategy mechanisms Section 2.4, then any e cient and iterative mechanism with incremental truth-revelation as a dominant strategy must compute the outcome of a Groves mechanism for the underlying preferences of agents. This is to avoid the existence of an equivalent direct-revelation mechanism for the mechanism that is outside of the class of Groves, which would be impossible. It is useful to characterize the computation in a mechanism within two distinct levels: 1. At the agent level: a Valuation complexity. How much computation is required to provide preference information within a mechanism? b Strategic complexity. Must agents model other agents and solve game-theoretic problems to compute an optimal strategy? 2. At the infrastructure level: a Winner-determination complexity. How much computation is expected of the mechanism infrastructure, for example to compute an outcome given information provided by agents? b Communication complexity. How much communication is required, between agents and the mechanism, to compute an outcome? Dominant strategy mechanisms, such as the Groves mechanisms, are e cient and strategy-proof mechanisms, giving them excellent strategic complexity. An agent can compute a dominant-strategy without modeling the other agents and without game-theoretic reasoning. However, the direct-revelation property of Groves mechanisms provides very bad in fact worst-case agent valuation complexity. An optimal bidding strategy requires that an agent determines its complete preferences over all possible outcomes. Complete information is required in all instances, even though it is often possible to solve a particular instance with incomplete information, with an interactive solution such as that pr...
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This document was uploaded on 03/19/2014 for the course COMP CS286r at Harvard.

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