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40
Mechanism Design Over Discrete Domains
"... Often, we wish to design incentivecompatible algorithms for settings in which the players ’ private information is drawn from discrete domains (e.g., integer values). Our main result is identifying discrete settings in which an algorithm can be made incentivecompatible iff the function it computes ..."
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Often, we wish to design incentivecompatible algorithms for settings in which the players ’ private information is drawn from discrete domains (e.g., integer values). Our main result is identifying discrete settings in which an algorithm can be made incentivecompatible iff the function it computes upholds a simple monotonicity constraint, known as weakmonotonicity. To the best of our knowledge, this is the first such characterization of incentivecompatibility in discrete domains (such characterizations were previously known only for inherently nondiscrete domains, e.g., convex domains). We demonstrate the usefulness of this result by showing an application to the TCPinspired congestioncontrol problem presented in [19].
Using Mechanism Design to Prevent FalseName Manipulations
"... 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 falsename manipulations have traditionally not been considered in the ..."
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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 falsename 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 falsenameproofness. 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
Two Simplified Proofs for Roberts ’ Theorem
"... Roberts (1979) showed that every social choice function that is expost 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 keypoint, but significant ..."
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Roberts (1979) showed that every social choice function that is expost 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 keypoint, 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
Monotonicity and Implementability
"... Consider an environment with a finite number of alternatives, and agents with private values and quasilinear utility functions. A domain of valuation functions for an agent is a monotonicity domain if every finitevalued monotone randomized allocation rule defined on it is implementable in dominant ..."
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Consider an environment with a finite number of alternatives, and agents with private values and quasilinear utility functions. A domain of valuation functions for an agent is a monotonicity domain if every finitevalued monotone randomized allocation rule defined on it is implementable in dominant strategies. We fully characterize the set of all monotonicity domains.
Falsenameproofness with Bid Withdrawal
"... We study a more powerful variant of falsename manipulation in Internet auctions: an agent can submit multiple falsename bids, but then, once the allocation and payments have been decided, withdraw some of her falsename identities (have some of her falsename identities refuse to pay). While these ..."
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We study a more powerful variant of falsename manipulation in Internet auctions: an agent can submit multiple falsename bids, but then, once the allocation and payments have been decided, withdraw some of her falsename 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 falsenameproof with withdrawal (FNPW) if the aforementioned manipulation is never beneficial. FNPW is a stronger condition than falsenameproofness (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 worstcase efficiency ratio of FNPW mechanisms. In the appendix, we give a characterization of FNP(W) social choice rules. 1.
An impossibility result for expost implementable multiitem auctions with private values
, 2007
"... We analyze expost implementable social choice functions for privatevalue and quasilinear settings over restricted domains of preferences, the leading example being multiitem auctions (with either heterogeneous or homogeneous goods). Our work generalizes the characterization of Roberts (1979) who ..."
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We analyze expost implementable social choice functions for privatevalue and quasilinear settings over restricted domains of preferences, the leading example being multiitem auctions (with either heterogeneous or homogeneous goods). Our work generalizes the characterization of Roberts (1979) who characterized expost implementability over unrestricted domains. We show that expost implementability for multiitem auctions (and related restricted domains) implies weighted welfare maximization, if the given function also satisfies four additional social choice requirements. The most significant requirement is similar to Arrow’s IIA condition, adjusted to the quasilinear case, and we study its connection to various existing monotonicity properties.
Information and communication in mechanism design
, 2006
"... September 2006This work was carried out under the supervision of ..."
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September 2006This work was carried out under the supervision of
Revenue Monotonicity in Deterministic, DominantStrategy Combinatorial Auctions
, 2009
"... In combinatorial auctions using VCG, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this counterintuitive phenomenon can also occur under other deterministic dominantstrategy combinatorial auction mechanisms. Our main result is that su ..."
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In combinatorial auctions using VCG, a seller can sometimes increase revenue by dropping bidders. In this paper we investigate the extent to which this counterintuitive phenomenon can also occur under other deterministic dominantstrategy 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 singleminded preferences. We also give a set of other impossibility results as corollaries, concerning revenue when the set of goods changes, falsenameproofness, and the core.
Improved Lower Bounds for NonUtilitarian Truthfulness ∗
"... One of the most fundamental results in the field of mechanism design states that every utilitarian social choice function admits a mechanism that truthfully implements it. In stark contrast with this finding, when one considers a nonutilitarian social choice function, it turns out that no guarantee ..."
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One of the most fundamental results in the field of mechanism design states that every utilitarian social choice function admits a mechanism that truthfully implements it. In stark contrast with this finding, when one considers a nonutilitarian social choice function, it turns out that no guarantees can be made, i.e. there are nonutilitarian functions, which cannot be truthfully implemented. In light of this state of affairs, one of the most natural and intriguing objectives of research is to understand the inherent limitations in the infrastructure of truthful mechanisms for nonutilitarian social choice functions. In this paper, we focus our attention on studying the boundaries imposed by truthfulness for two nonutilitarian multiparameter optimization problems. The first is the workload minimization in interdomain routing problem, which models one of the most principle problems in the design of routing protocols, and the other is the unrelated machines scheduling problem, which is one of the most classical and general variants in the field of scheduling. Our main findings can be briefly summarized as follows: 1. We prove that any truthful deterministic mechanism, and any universal truthful randomized mechanism for the workload minimization in interdomain routing problem cannot achieve an approximation guarantee that is better than 2. These results improve the current lower bounds of (1 + √ 5)/2 ≈ 1.618 and (3 + √ 5)/4 ≈ 1.309, which are due to Mu’alem and Schapira [SODA ’07]. 2. We establish a lower bound of 1 + √ 2 ≈ 2.414 on the achievable approximation ratio of any truthful deterministic mechanism for the unrelated machines scheduling problem when the number of machines is at least 3. This lower bound is comparable to a recent result by Christodoulou, Koutsoupias and Vidali [SODA ’07]. Nevertheless, our approach is considerably simpler, and thus may shed some new light on the foundations of this problem.
Uncertainty in Mechanism Design
, 2006
"... 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 thi ..."
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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 expost 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.