We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks; in particular, we restrict attention to mechanisms where users are restricted to one-dimensional strategy spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate. We study the worst-case efficiency loss (ratio of the utility associated with a Nash equilibrium to the maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price differentiation is permitted; using an adaptation of the Vickrey-Clarke-Groves class of mechanisms, we construct a class of mechanisms with one-dimensional strategy spaces where Nash equilibria are fully efficient. These mechanisms are shown to be fully efficient even in general convex environments, under reasonable assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually improve the efficiency guarantee.

We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. 1

We study the computational power of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items, and querying the bidders for their “demand” under these prices. We prove several results regarding such auctions that use a polynomial number of demand queries: (1) that such auctions can simulate several other natural types of queries; (2) that they can approximate the optimal allocation as well as generally possible using polynomial communication or computation, while weaker types of queries cannot do so; (3) that such auctions that only use item prices may solve allocation problems in communication cost that is exponentially lower than the cost incurred by auctions that use prices for bundles. For the latter result, we initiate the study of how prices of bundles can be represented when they are not linear, and show that the “default” representation has severe limitations. Our results hold for any series of demand queries with polynomial length, without any additional restrictions on the queries (e.g., to ascending prices).

We consider the amount of communication required to verify the outcome of the Vickrey-Clarke-Groves (VCG) mechanism: an efficient allocation together with incentivizing VCG payments. We compare this to the communication required to verify the efficient decision rule alone, to assess the overhead imposed by VCG payments. Our characterizations are obtained by leveraging a connection between the VCG outcome and a price equilibrium concept known as universal competitive equilibrium. We consider four related environments within a common framework: the classic single-item setting, the multi-unit setting with decreasing marginal values, the classic assignment problem with unitdemand valuations, and the multi-unit assignment problem with substitutes valuations. We find that the single-unit settings have zero overhead, whereas the multi-unit settings can have significant positive overhead. With multiple units, the naïve VCG protocol that runs several efficient protocols in sequence (one with all agents, and ones with an agent removed, for each agent) is asymptotically optimal for several parameter settings of the number of agents, commodities, and units.

Collusion, privacy, and beliefs are forces uniquely capable of affecting the play of a mechanism. In this paper, we define a class of mechanisms totally resilient to these three forces, and then prove that one such mechanism essentially maximizes social welfare in a budget-balanced way. Our mechanism works in markets where the players have complete information about each other’s utilities (but not about who colludes with whom), meaningfully bypasses classical impossibility results, and enjoys other valuable properties. In particular, it requires a minimal amount of communication. 1

September 2006This work was carried out under the supervision of

... for certain applications. Experimental results demonstrate that the elicitation framework can complement current designs by allowing for alternate representations where XOR is inappropriate, resulting in fewer queries and faster convergence. The framework consists of elicitation, allocation, and pricing engines. The pricing engine is also modular. I present two different methods for pricing, one of which can also serve as a stand-alone iterative auction. The auction begins with item prices and introduces bundle prices as needed to drive the bidding forward. This again complements existing designs which are limited to XOR or item pricing. The framework can also be extended to compute VCG payments, to bring truthful responses to queries into an equilibrium.

In this note we give a survey of bisection auctions. Bisection auctions have been introduced in order to reduce the number of rounds and increase privacy of information in iterative implementations of Vickrey auctions. First, we present the case of discrete valuations. we discuss the strategic properties of this auction and recent results which show that—for 2 bidders—the auction dominates in a particular sense any other auction with respect to the number of bits revealed. For the case of continuous valuations we contrast its properties with the result that no practical query auction can achieve full efficiency in ex-post equilibrium.

In the presence of self-interested parties, mechanism designers typically aim to achieve their goals (implement a social-choice function) in an equilibrium. In this paper, we study the cost of such equilibrium requirements in terms of communication, a problem that was recently raised by Fadel and Segal (2009). While a certain amount of information x needs to be communicated just for computing the outcome of a certain social-choice function, an additional amount of communication may be required for computing the equilibrium-supporting payments (when such payments exist). Our main result shows that the total amount of information required for this task can be greater than x by a factor linear in the number of players n, i.e., n · x (under a common normalization assumption). This is the first known lower bound for this problem. In fact, we show that this result holds even in single-parameter domains. On the positive side, we show that certain classic economic domains, namely, single-item auctions and public-good mechanisms, only entail a small overhead. Finally, we discuss the case in which the normalization assumption does not hold and leave the readers with several open questions.

We consider two alternatives to optimal auctions: posted-price mechanisms and dynamic auctions. In posted-price mechanisms, the seller posts a single price and sells the item at this price to a bidder that accepts it. In a dynamic auction, bidders arrive sequentially and each bidder leaves the market before the next bidder arrives. We establish an exact asymptotic characterization of the optimal revenue in each of these mechanisms for general distributions, under a mild condition taken from extreme-value theory. We also devise postedprice and dynamic mechanisms that achieve this optimal revenue. Intuitively, one would expect auctions to perform better compared to posted prices as the values of the bidders are more dispersed; We show that this intuition holds up to a point where more value dispersion causes an opposite phenomenon. Our results also imply that such mechanisms may lose a non-trivial share of the optimal-auction revenue, even in large markets.