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Abstract not found

In combinatorial auctions using VCG, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this counter-intuitive phenomenon can also occur under other deterministic dominant-strategy combinatorial auction mechanisms. Our main result is that such failures of “revenue monotonicity” can occur under any such mechanism that is weakly maximal—meaning roughly that it chooses allocations that cannot be augmented to cause a losing bidder to win without hurting winning bidders—and that allows bidders to express arbitrary single-minded preferences. We also give a set of other impossibility results as corollaries, concerning revenue when the set of goods changes, false-name-proofness, and the core.

In combinatorial auctions that use VCG, a seller can sometimes increase revenue by dropping bidders (see e.g. [5]). In our previous work [26], we showed that such failures of “revenue monotonicity ” occur under an extremely broad range of deterministic strategyproof combinatorial auction mechanisms, even when bidders have “known single-minded ” valuations. In this work we consider the question of whether revenue monotonic, strategyproof mechanisms for such bidders can be found in the broader class of randomized mechanisms. We demonstrate that—surprisingly—such mechanisms do exist, show how they can be constructed, and consider algorithmic techniques for implementing them in polynomial time. More formally, we characterize a class of randomized mechanisms defined for known single-minded bidders that are strategyproof and revenue monotonic, and furthermore satisfy some other desirable properties, namely participation, consumer sovereignty and maximality, representing the mechanism as a solution to a quadratically constrained linear program (QCLP). We prove that the QCLP is always feasible (i.e., for all bidder valuations) and give its solution analytically. Furthermore, we give an algorithm for running such a mechanism in time polynomial in the number of bidders and goods; this is interesting because constructing an instance of such mechanisms from our QCLP formulation in a naive way can require exponential time. 1

We describe here a structured system for distributed mechanism design appropriate for the Internet applications. In our approach the players dynamically form a network in which they know neither their neighbours nor the size of the network and interact to jointly take decisions. The only assumption concerning the underlying communication layer is that for each pair of processes there is a path of neighbours connecting them. This allows us to deal with arbitrary network topologies. We also discuss the implementation of this system which consists of a sequence of layers. The lower layers deal with the operations relevant for distributed computing only, while the upper layers are concerned only with communication among players, including broadcasting and multicasting, and distributed decision making. This yields a highly flexible distributed system whose specific applications are realized as instances of its top layer. This design is implemented in Java. The system supports fault-tolerance and can be augmented by a provision for distributed policing the purpose of which is to exclude ‘dishonest ’ players. Also, it can be used for repeated creation of dynamically formed networks of players interested in a joint decision making implemented by means of a tax-based mechanism. We illustrate its flexibility by discussing a number of implemented examples.