We study a class of single-round, sealed-bid auctions for items in unlimited supply, such as digital goods. We introduce the notion of competitive auctions. A competitive auction is truthful (i.e., encourages buyers to bid their utility) and yields profit that is roughly within a constant factor of the profit of optimal fixed pricing for all inputs. We justify the use of optimal fixed pricing as a benchmark for evaluating competitive auction profit. We show that several randomized auctions are truthful and competitive and that no truthful deterministic auction is competitive. Our results extend to bounded supply markets, for which we also get truthful and competitive auctions.

... in networks. We consider a model of selfish routing in which the latency experienced by network tra#c on an edge of the network is a function of the edge congestion, and network users are assumed to selfishly route tra#c on minimum-latency paths. The quality of a routing of tra#c is historically measured by the sum of all travel times, also called the total latency. It is well known

Mechanism design is now a standard tool in computer science for aligning the incentives of self-interested agents with the objectives of a system designer. There is, however, a fundamental disconnect between the traditional application domains of mechanism design (such as auctions) and those arising in computer science (such as networks): while monetary transfers (i.e., payments) are essential for most of the known positive results in mechanism design, they are undesirable or even technologically infeasible in many computer systems. Classical impossibility results imply that the reach of mechanisms without transfers is severely limited. Computer systems typically do have the ability to reduce service quality—routing systems can drop or delay traffic, scheduling protocols can delay the release of jobs, and computational payment schemes can require computational payments from users (e.g., in spam-fighting systems). Service degradation is tantamount to requiring that users burn money, and such “payments ” can be used to influence the preferences of the agents at a cost of degrading the social surplus. We develop a framework for the design and analysis of money-burning mechanisms to maximize the residual surplus— the total value of the chosen outcome minus the payments required. Our primary contributions are the following. • We define a general template for prior-free optimal mechanism design that explicitly connects Bayesian optimal mechanism design, the dominant paradigm in economics, with worst-case analysis. In particular, we establish a general and principled way to identify appropriate performance benchmarks in prior-free mechanism design. • For general single-parameter agent settings, we char-

We present and discuss general techniques for proving inapproximability results for truthful mechanisms. We make use of these techniques to prove lower bounds on the approximability of several non-utilitarian multi-parameter problems. In particular, we demonstrate the strength of our techniques by exhibiting a lower bound of 2 − 1 m for the scheduling problem with unrelated machines (formulated as a mechanism design problem in the seminal paper of Nisan and Ronen on Algorithmic Mechanism Design). Our lower bound applies to truthful randomized mechanisms (disregarding any computational assumptions on the running time of these mechanisms). Moreover, it holds even for the weaker notion of truthfulness for randomized mech-anisms – i.e., truthfulness in expectation. This lower bound nearly matches the known 7 4 (randomized) truthful upper bound for the case of two machines (a non-truthful FPTAS exists). No lower bound for truthful randomized mechanisms in multi-parameter settings was previously known. We show an application of our techniques to the workload-minimization problem in networks. We prove our lower bounds for this problem in the inter-domain routing setting presented by Feigenbaum, Papadimitriou, Sami, and Shenker. Finally, we discuss several notions of non-utilitarian “fairness ” (Max-Min fairness, Min-Max fairness, and envy minimization). We show how our techniques can be used to prove lower bounds for these notions.

The monopolist’s theory of optimal single-item auctions for agents with independent private values can be summarized by two statements. The first is from Myerson [8]: the optimal auction is Vickrey with a reserve price. The second is from Bulow and Klemperer [1]: it is better to recruit one more bidder and run the Vickrey auction than to run the optimal auction. These results hold for single-item auctions under the assumption that the agents ’ valuations are independently and identically drawn from a distribution that satisfies a natural (and prevalent) regularity condition. These fundamental guarantees for the Vickrey auction fail to hold in general single-parameter agent mechanism design problems. We give precise (and weak) conditions under which approximate analogs of these two results hold, thereby demonstrating that simple mechanisms remain almost optimal in quite general single-parameter agent settings.

We propose novel solutions for unicast routing in wireless networks consisted of selfish terminals: in order to alleviate the inevitable over-payment problem (and thus economic inefficiency) of the VCG (Vickrey-Clark-Groves) mechanism, we design a mechanism that results in Nash equilibria rather than the traditional strategyproofness (using weakly dominant strategy). In addition, we systematically study the unicast routing system in which both the relay terminals and the service requestor (either the source or the destination nodes or both) could be selfish. To the best of our knowledge, this is the first paper that presents social efficient unicast routing systems with proved performance guarantee. Thus, we call the proposed systems: Optimal Unicast Routing Systems (OURS). Our main contributions of OURS are as follows. (1) For the principal model where the service requestor is not selfish, we propose a

Abstract. We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor’s prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game. We analyze the complexity and approximability of the first player’s best strategy in StackMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most min{k, 3 + 2 ln b, 1 + ln W}, where k is the number of distinct red costs, b is the number of blue edges, and W is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm. 1

We introduce revenue submodularity, the property that market expansion has diminishing returns on an auction’s expected revenue. We prove that revenue submodularity is generally possible only in matroid markets, that Bayesian-optimal auctions are always revenue-submodular in such markets, and that the VCG mechanism is revenue-submodular in matroid markets with i.i.d. bidders and “sufficient competition”. We also give two applications of revenue submodularity: good approximation algorithms for novel market expansion problems, and approximate revenue guarantees for the VCG mechanism with i.i.d. bidders.

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Prosper, the largest online social lending marketplace with nearly a million members and $178 million in funded loans, uses an auction amongst lenders to finance each loan. In each auction, the borrower specifies D, the amount he wants to borrow, and a maximum acceptable interest rate R. Lenders specify the amounts ai they want to lend, and bid on the interest rate, bi, they’re willing to receive. Given that a basic premise of social lending is cheap loans for borrowers, how does the Prosper auction do in terms of the borrower’s payment, when lenders are strategic agents with private true interest rates? The Prosper mechanism is exactly the same as the VCG mechanism applied to a modified instance of the problem, where lender i is replaced by ai dummy lenders, each willing to lend one unit at interest rate bi. However, the two mechanisms behave very differently — the VCG mechanism is truthful, whereas Prosper is not, and the total payment of the borrower can be vastly different in the two mechanisms. We first provide a complete analysis and characterization of the Nash equilibria of the Prosper mechanism. Next, we show that while the borrower’s payment in the VCG mechanism is always within a factor of O(log D) of the payment in any equilibrium of Prosper, even the cheapest Nash equilibrium of the Prosper mechanism can be as large as a factor D of the VCG payment; both factors are tight. Thus, while the Prosper mechanism is a simple uniform price mechanism, it can lead to much larger payments for the borrower than the VCG mechanism. Finally, we provide a model to study Prosper as a dynamic auction, and give tight bounds on the price for a general class of bidding strategies.