We consider mechanism design problems with Knightian uncertainty formalized using incomplete preferences, as in Bewley (1986). Without completeness, decision making depends on a set of beliefs, and an action is preferred to another if and only if it has larger expected utility for all beliefs in this set. We consider two natural notions of incentive compatibility in this setting: maximal incentive compatibility requires that no strategy has larger expected utility than reporting truthfully for all beliefs, while optimal incentive compatibility requires that reporting truthfully has larger expected utility than all other strategies for all beliefs. In a model with a continuum of types, we show that optimal incentive compatibility is equivalent to ex-post incentive compatibility under fairly general conditions on beliefs. In a model with a discrete type space, we characterize full extraction of rents generated from private information. We show that full extraction is generically possible with maximal incentive compatible mechanisms, but requires sufficient disagreement across types, which neither holds nor fails generically, with optimal incentive compatible mechanisms.

The existence of incentive-compatible computationally-efficient protocols for combinatorial auctions with decent approximation ratios is the paradigmatic problem in computational mechanism design. It is believed that in many cases good approximations for combinatorial auctions may be unattainable due to an inherent clash between truthfulness and computational efficiency. However, to date, researchers lack the machinery to prove such results. In this paper, we present a new approach: We take the first steps towards the development of new technologies for lower bounding the VC-dimension of k-tuples of disjoint sets. We apply this machinery to prove the first computational-complexity inapproximability results for incentive-compatible mechanisms for combinatorial auctions. These results hold for the important class of VCG-based mechanisms, and are based on the complexity assumption that NP has no polynomial-size circuits. We believe that our approach holds great promise. Indeed, subsequently to our work, Buchfuhrer and Umans [10], and, independently, Dughmi et al. [20], strengthened our results via extensions of our techniques, thus proving conjectures we presented in [32]

We study a more powerful variant of false-name manipulation in Internet auctions: an agent can submit multiple false-name bids, but then, once the allocation and payments have been decided, withdraw some of her false-name identities (have some of her falsename identities refuse to pay). While these withdrawn identities will not obtain the items they won, their initial presence may have been beneficial to the agent’s other identities. We define a mechanism to be false-name-proof with withdrawal (FNPW) if the aforementioned manipulation is never beneficial. FNPW is a stronger condition than false-name-proofness (FNP). We first give a necessary and sufficient condition on the type space for the VCG mechanism to be FNPW. We then characterize both the payment rules and the allocation rules of FNPW mechanisms in general combinatorial auctions. Based on the characterization of the payment rules, we derive a condition that is sufficient for a mechanism to be FNPW. We also propose the maximum marginal value item pricing (MMVIP) mechanism. We show that MMVIP is FNPW and exhibit some of its desirable properties. We then propose an automated mechanism design technique that transforms any feasible mechanism into an FNPW mechanism, and prove some basic properties about this technique. Since FNPW is stronger than FNP, the mechanisms we obtain in this paper are also FNP. Finally, we prove a strict upper bound on the worst-case efficiency ratio of FNPW mechanisms. In the appendix, we give a characterization of FNP(W) social choice rules. 1.

September 2006This work was carried out under the supervision of

When mechanisms such as auctions, rating systems, and elections are run in a highly anonymous environment such as the Internet, a key concern is that a single agent can participate multiple times by using false identifiers. Such false-name manipulations have traditionally not been considered in the theory of mechanism design. In this article, we review recent efforts to extend the theory to address this. We first review results for the basic concept of false-name-proofness. Because some of these results are very negative, we also discuss alternative models that allow us to circumvent some of these negative results. Technologies such as the Internet allow many spatially distributed parties (or agents) to rapidly interact according to intricate protocols. Some of the most exciting applications

Roberts (1979) showed that every social choice function that is ex-post implementable in private value settings must be weighted VCG, i.e. it maximizes the weighted social welfare. This paper provides two simplified proofs for this. The first proof uses the same underlying key-point, but significantly simplifies the technical construction around it, thus helps to shed light on it. The second proof builds on monotonicity conditions identified by Rochet [11] and Bikhchandani et. al. [2]. This proof is for a weaker statement that assumes an additional condition of “player decisiveness”. 1

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.

Consider an environment with a finite number of alternatives, and agents with private values and quasi-linear utility functions. A domain of valuation functions for an agent is a monotonicity domain if every finite-valued monotone randomized allocation rule defined on it is implementable in dominant strategies. We fully characterize the set of all monotonicity domains.

We study the online version of the classical parallel machine scheduling problem to minimize the total weighted completion time from the perspective of algorithmic mechanism design. We assume that the data of each job, namely its release date rj, its processing time pj and its weight wj is only known to the job itself, but not to the system. In communicating with the system, selfish jobs may thus be tempted to manipulate the outcome by lying. Furthermore, we assume a setting without any central scheduling or routing unit. Instead we assume that the jobs themselves need to choose the machine on which they want to be processed. In this context, we introduce the concept of a myopic best response equilibrium, a concept weaker than the classical dominant strategy equilibrium, but appropriate for online problems. We present a polynomial time, online scheduling mechanism that, assuming rational behavior of jobs, results in an equilibrium schedule that is 3.281-competitive. The mechanism deploys a very intuitive online payment scheme that induces rational jobs to truthfully report their private data. We also show that the underlying allocation of jobs to machines, which we actually need in order to prove the performance bound, cannot be extended to a mechanism where truthful reports constitute a dominant strategy equilibrium.

Theoretical study and simulation of algorithms in strategic environments, especially problems arising in the design of resource allocation problems, auctions with multiple goods and scheduling