Computational Mechanism Design Chapter 3

In addition to the network resource cost this might

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Unformatted text preview: information to the auctioneer. In addition to the network resource cost, this might be undesirable from a privacy perspective. A number of proposals exist to address each of these problems, surveyed below. The rst problem, concerning the computational complexity of the auctioneer's winner determination problem, has received most attention. In comparison, the second problem, concerning the complexity on participants to determine their preferences has received considerably less attention. Exceptions include the brief discussion of bidding programs in Nisan Nis00 , and the recent progress that has been made on dynamic mechanisms WW00, Par99, PU00b . This dynamic approach includes my iBundle mechanism, and recent extensions to compute Vickrey payments. iBundle is an iterative combinatorial auction mechanism, able to compute e cient allocations without complete information revelation from agents. The information savings follow from an equilibrium-based interactive solution concept, in which the e cient allocation is computed in an equilibrium between the auctioneer and the agents. In addition to terminating without complete information revelation in realistic problem instances, agents in iBundle can compute optimal strategies without solving their complete local valuation problems. 66 3.2.1 Winner-Determination: Approximations and Distributed Methods Possible ideas to address the complexity of winner-determination in the GVA include introducing approximation, identifying and restricting to special-cases, and distributed methods that seek to involve decentralized agents in the mechanism's computational problem. In each case, as new methods are used to compute the outcome of a Groves mechanism, it is important to consider the e ect on the strategy-proofness of the mechanism. There are two reasons to be concerned about the loss of strategy-proofness with an approximate Groves mechanism: | agents can now bene t from game-theoretic reasoning, which makes their strategic bidding problem more di cult | the e ect of agents misrepresenting their preferences might further decrease the allocative-e ciency. Approximations Simply replacing the optimal algorithm in the GVA with an approximation algorithm does not preserve strategy-proofness. Recall that the utility to agent i in the GVA for reported ^ preferences i , is: ^ ^^ ui i = vik  i; ,i; i  + X v k ^ ; ^ j 6=i ^ ^ i ,i ; j  , hi  ,i  j ^ ^ ^^ where hi  is an arbitrary function over the reported preferences ,i =  1 ; : : : ; i,1 ; i+1 ; ^ : : : ; I  of the other agents. ^ ^^ Agent i chooses to announce preferences i to make k  i ; ,i  solve: max vi k; i  + k2K X v k; ^  j 6=i j j * ^^ Truth-revelation is a dominant strategy in the GVA because k  i ; ,i  solves this ^ problem with i = i . With an approximate winner-determination algorithm the auctioneer selects outcome ^^ ^ ^^ ^ k i; ,i , which might not equal k  i; ,i. A rational agent will now announce a type i to try to make the approximation algorithm solve *: 67 ^^ k i; ,i = k  i; ,i In other words, the agent would like to make the approximation algorithm select the best possible outcome, given its true preferences and the announced preferences of the other agents, and this might perhaps be achieve...
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