We study auctions with severe bounds on the communication allowed: each bidder may only transmit Ø bits of information to the auctioneer. We consider both welfaremaximizing and revenue-maximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove nonsurprising properties of these kinds of auctions, e.g. that discrete prices are informationally efficient, as well as some surprising properties, e.g. that asymmetric auctions are better than symmetric ones.
We consider exchange economies, where the initial endowment of each agent consists of some set of resources. The private information of the agents is their value for every possible subset of all the resources. The goal is to redistribute resources among agents to maximize efficiency, where monetary transfers are allowed. As agents may simultaneously play the role of buyers and sellers, the standard method for implementing efficient outcomes -VCG mechanisms -may not be budget balanced. In fact, it is known (Myerson and Satterthwaite, 1983) that even in the simplest bilateral-trade setting no mechanism can simultaneously achieve full efficiency, individual rationality and budget balance in (Bayes Nash) equilibrium.In this paper, we develop incentive-compatible, individually-rational and budget balanced mechanisms for several classic settings. All our mechanisms (except one) provide a constant approximation to the optimal efficiency in these settings, even in ones where the preferences of the agents are complex multi-parameter functions. Some of our mechanisms achieve approximation guarantee in expectation, given prior distributions on the preferences of the agents, and other approximation results hold for every realization of the preferences.We start with analyzing the simple one-buyer one-seller bilateral trade setting, where some design challenges start revealing. We present a mechanism that achieves in expectation at least half of the expected value of the efficient allocation. We then show how this mechanism can be used to achieve the same approximation ratio for the more general Partnership Dissolving setting, where several agents initially hold fractions of a divisible item.Both bilateral trade and partnership dissolving are single-parameter domains. Our main technical results are two mechanisms for more complex multi-parameter domains. The first domain is combinatorial exchange, where a set of m indivisible heterogeneous items is initially distributed among the agents. Agents have combinatorial sub-additive preferences. We show that there exists a truthful, individually rational, weakly budget balanced mechanism that provides an 8Hm-approximation to the optimal welfare (where Hm is the m'th harmonic number). Our second multi-parameter domain is the classic exchange model of Arrow and Debreu, where agents have concave valuation functions for a single divisible good. We devise a truthful, prior-free, individually rational, weakly budget balanced mechanism that provides a constant approximation to the optimal social welfare (as long as no single agent holds a huge chunk of the good).
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