Computational Mechanism Design Chapter 3

71 an interesting idea for future work is to design

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Unformatted text preview: umption of myopia considerably simpli es an agent's problem, as it does not need to reason about the e ect of its bids in the current round on future prices or on the strategies of other agents. 71 An interesting idea for future work is to design mechanisms that cannot be manipulated unless an agent can solve an NP-hard computational problem; i.e. use the boundedratonality of an agent to make it provably too di cult to manipulate a mechanism. Special-Cases and Structure Finally, let us consider the role of tractable special-cases of winner-determination. Rothkopf et al. RPH98 , Nisan Nis00 and de Vries & Vohra dVV00 characterize tractable specialcases, identifying restrictions on the types of bundles that can receive bids and or the types of valuation functions agents can express over bundles see Section 4.5. The approach is to restrict an agent's bidding language to induce only tractable winner-determination problems. Ideally, a restricted bidding language can support tractable winner-determination without preventing agents reporting their true valuation functions. In this case the GVA mechanism can be applied without any loss in either strategy-proofness or e ciency. However, as soon as one imposes a restriction on agents' bids there is a risk that e ciency and strategyproofness will be compromised. If an agent cannot represent its true valuation function with the restricted bidding language, then its rational strategy is to report an approximate value that leads to the best outcome for its true preferences, and force the mechanism to select the best solution from the set reachable from the restricted range of inputs. This ability to improve the outcome through non-truthful bidding leads to a loss in strategyproofness, for example because the agent will now need to predict the strategies of other agents. The tradeo between approximate bidding languages, incentive-compatibility, and e ciency appears to have received little attention. Graphical tree representations, such as the Expected Utility Networks MS99 , allow an agent to capture independence structure within its preferences in much the same way as Bayes-Nets provide compact representations of conditional probabilities in suitable problems. In addition to providing quite compact and natural representations for participants, these structured approaches may allow tractable winner-determination and payment rules, that exploit the structure to solve problems without explicitly computing values for individual bundles. 72 3.2.2 Valuation Complexity: Bidding Programs and Dynamic Methods The Groves mechanisms are direct-revelation mechanisms, requiring that every agent reports its complete preferences over all possible outcomes. In application to large combinatorial problems Groves mechanisms can fail because of the bounded-rationality of agents, and the complexity of local valuation problems. The valuation problem for a single bundle can be hard, and in combinatorial domains there are an exponential number of di erent bundles to consider. Consider an application to a distributed package delivery problem, with agents competing for the delivery jobs. Agents represent delivery companies, and may nee...
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This document was uploaded on 03/19/2014 for the course COMP CS286r at Harvard.

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