Results 1 
7 of
7
Towards more expressive cake cutting
 In Proc. 22nd IJCAI
, 2011
"... Abstract Cake cutting is a playful name for the problem of fairly dividing a heterogeneous divisible good among a set of agents. The agent valuations for different pieces of cake are typically assumed to be additive. However, in certain practical settings this assumption is invalid because agents m ..."
Abstract

Cited by 15 (8 self)
 Add to MetaCart
Abstract Cake cutting is a playful name for the problem of fairly dividing a heterogeneous divisible good among a set of agents. The agent valuations for different pieces of cake are typically assumed to be additive. However, in certain practical settings this assumption is invalid because agents may not have positive value for arbitrarily small "crumbs" of cake. In this paper, we propose a new, more expressive model of agent valuations that captures this feature. We present an approximately proportional algorithm for any number of agents that are endowed with these expressive valuations, which is optimal in the sense that no algorithm can guarantee a greater worstcase degree of proportionality. We also design an optimal approximately proportional and fully envy free algorithm for two agents.
An Expressive Mechanism for Auctions on the Web
 WWW 2011
, 2011
"... Auctions are widely used on the Web. Applications range from internet advertising to platforms such as eBay. In most of these applications the auctions in use are single/multiitem auctions with unit demand. The main drawback of standard mechanisms for this type of auctions, such as VCG and GSP, is t ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
Auctions are widely used on the Web. Applications range from internet advertising to platforms such as eBay. In most of these applications the auctions in use are single/multiitem auctions with unit demand. The main drawback of standard mechanisms for this type of auctions, such as VCG and GSP, is the limited expressiveness that they offer to the bidders. The General Auction Mechanism (GAM) of [1] is taking a first step towards addressing the problem of limited expressivenessbycomputingabidderoptimal, envyfree outcome for linear utility functions with identical slopes and a single discontinuity per bidderitem pair. We show that in many practical situations this does not suffice to adequately model the preferences of the bidders, and we overcome this problem bypresentingthefirst mechanism for piecewise linear
Valuation compressions in vcgbased combinatorial auctions
 In WINE
, 2013
"... Abstract The focus of classic mechanism design has been on truthful directrevelation mechanisms. In the context of combinatorial auctions the truthful directrevelation mechanism that maximizes social welfare is the VCG mechanism. For many valuation spaces computing the allocation and payments of ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
(Show Context)
Abstract The focus of classic mechanism design has been on truthful directrevelation mechanisms. In the context of combinatorial auctions the truthful directrevelation mechanism that maximizes social welfare is the VCG mechanism. For many valuation spaces computing the allocation and payments of the VCG mechanism, however, is a computationally hard problem. We thus study the performance of the VCG mechanism when bidders are forced to choose bids from a subspace of the valuation space for which the VCG outcome can be computed efficiently. We prove improved upper bounds on the welfare loss for restrictions to additive bids and upper and lower bounds for restrictions to nonadditive bids. These bounds show that the welfare loss increases in expressiveness. All our bounds apply to equilibrium concepts that can be computed in polynomial time as well as to learning outcomes.
Do Externalities Degrade GSP’s Efficiency?
, 2012
"... We consider variants of the cascade model of externalities in sponsored search auctions introduced independently by Aggrawal et al. and Kempe and Mahdian in 2008, where the clickthrough rate of a slot depends also on the ads assigned to earlier slots. Aggrawal et al. and Kempe and Mahdian give a dy ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We consider variants of the cascade model of externalities in sponsored search auctions introduced independently by Aggrawal et al. and Kempe and Mahdian in 2008, where the clickthrough rate of a slot depends also on the ads assigned to earlier slots. Aggrawal et al. and Kempe and Mahdian give a dynamic programming algorithm for finding the efficient allocation in this model. We give worstcase efficiency bounds for a variant of the classical Generalized Second Price (GSP) auction in this model. Our technical approach is to first consider an idealized version of the model where an unlimited number of ads can be displayed on the same page; here, Aggrawal et al. and Kempe and Mahdian show that a greedy algorithm finds the optimal allocation. The game theoretic analog of this greedy algorithm can be thought of as a variant of the classical GSP auction. We give the first nontrivial worstcase efficiency bounds for GSP in this model. In the more general model with limited slots, greedy algorithms like GSP can compute extremely bad allocations. Nonetheless, we show that an appropriate extension of the greedy algorithm is approximately optimal, and that the worstcase equilibrium inefficiency in the corresponding analog of GSP also remains bounded. In the context of these models, the GSP mechanisms suffer from two forms of suboptimality: that from using a simple allocation rule (the greedy algorithm) rather than an optimal one (based on dynamic programming), and that from the strategic behavior of the bidders (caused by using the GSP’s critical bid pricing rule rather than one leading to a dominantstrategy implementation). Our results show that for this class of problems, the two causes of efficiency loss can be analyzed separately.
Efficient advert assignment
, 2015
"... Abstract We develop a framework for the analysis of largescale Adauctions where adverts are assigned over a continuum of search types. For this payperclick market, we provide an efficient mechanism that maximizes social welfare. In particular, we show that the social welfare optimization can be ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract We develop a framework for the analysis of largescale Adauctions where adverts are assigned over a continuum of search types. For this payperclick market, we provide an efficient mechanism that maximizes social welfare. In particular, we show that the social welfare optimization can be solved in separate optimizations conducted on the timescales relevant to the search platform and advertisers. Here, on each search occurrence, the platform solves an assignment problem and, on a slower timescale, each advertiser submits a bid which matches its demand for clickthroughs with supply. Importantly, knowledge of global parameters, such as the distribution of search terms, is not required when separating the problem in this way. Exploiting the information asymmetry between the platform and advertiser, we describe a simple mechanism which incentivizes truthful bidding and has a unique Nash equilibrium that is socially optimal, and thus implements our decomposition. Further, we consider models where advertisers adapt their bids smoothly over time, and prove convergence to the solution that maximizes social welfare. Finally, we describe several extensions which illustrate the flexibility and tractability of our framework.
Expressiveness and Robustness of FirstPrice Position Auctions∗
"... Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized firstprice mechanism with multidimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are onedimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multidimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why firstprice payments may be able to support equilibria in a wider range of circumstances than secondprice payments. 1
Simple Position Auctions and Approximate Full Implementation?
"... Abstract. We consider a standard position auction setting and seek simple mechanisms that obtain the truthful outcome of the VCG mechanism in some equilibrium and high revenue in every equilibrium. Here, a simple mechanism is one that solicits a single, onedimensional bid from each agent which is ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We consider a standard position auction setting and seek simple mechanisms that obtain the truthful outcome of the VCG mechanism in some equilibrium and high revenue in every equilibrium. Here, a simple mechanism is one that solicits a single, onedimensional bid from each agent which is then multiplied by a fixed vector α to obtain bids for the different positions. Under complete information a generalized secondprice mechanism with α = (1,..., 1) guarantees revenue at least half the truthful VCG revenue for all positions but the first. This improves on earlier work, which had respectively shown the same bound for efficient equilibria of the same mechanism and for equilibria of a mechanism where α corresponds to the true relative values of the positions. Under incomplete information, a generalized firstprice mechanism, again with α = (1,..., 1), obtains the truthful VCG outcome in its unique equilibrium. 1