Anat Lerner

Profit maximizing in auctions of public goods

A profit-maximizing auctioneer can provide a public good to a group of agents. Each group member has a private value for the good being provided to the group. We investigate an auction mechanism where the auctioneer provides the good to the group, only if the sum of their bids exceeds a reserve price declared previously by the auctioneer. For the two-bidder case with private values drawn from a uniform distribution we characterize the continuously differentiable symmetric equilibrium bidding functions for the agents, and find the optimal reserve price for the auctioneer when such functions are used by the bidders. We also examine another interesting family of equilibrium bidding functions for this case, with a discrete number of possible bids, and show the relation (in the limit) to the differentiable bidding functions.

The Incompatibility of Pareto Optimality and Dominant-Strategy Incentive Compatibility in Sufficiently-Anonymous Budget-Constrained Quasilinear Settings

We analyze the space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal combinatorial auctions. We examine a model with multidimensional types, nonidentical items, private values and quasilinear preferences for the players with one relaxation; the players are subject to publicly-known budget constraints. We show that the space includes dictatorial mechanisms and that if dictatorial mechanisms are ruled out by a natural anonymity property, then an impossibility of design is revealed. The same impossibility naturally extends to other abstract mechanisms with an arbitrary outcome set if one maintains the original assumptions of players with quasilinear utilities, public budgets and nonnegative prices.

Dictatorial Mechanisms in Constrained Combinatorial Auctions

Abstract We study the possibility space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient combinatorial auctions in a model with two players and two nonidentical items (four outcomes). Our model has multidimensional types, private values, nonnegative prices, and quasilinear preferences for the players with one relaxation – the players are subject to publicly known budget constraints. We show that the space we study essentially includes one type of mechanisms: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto efficient. The mechanisms in the autocratic families are identical except for two to three price parameters that differentiate them.

Characterizing the Incentive Compatible and Pareto Optimal Efficiency Space for Two Players, k Items, Public Budget and Quasilinear Utilities

We characterize the efficiency space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto-optimal combinatorial auctions in a model with two players and k nonidentical items. We examine a model with multidimensional types, private values and quasilinear preferences for the players with one relaxation: one of the players is subject to a publicly known budget constraint. We show that if it is publicly known that the valuation for the largest bundle is less than the budget for at least one of the players, then Vickrey-Clarke-Groves (VCG) uniquely fulfills the basic properties of being deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal. Our characterization of the efficient space for deterministic budget constrained combinatorial auctions is similar in spirit to that of Maskin 2000 for Bayesian single-item constrained efficiency auctions and comparable with Ausubel and Milgrom 2002 for non-constrained combinatorial auctions.

Autocratic Mechanisms: A Form of Dictatorship in Constrained Combinatorial Auctions

We characterize the space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions where efficiency is not required. We examine a model with two players and k nonidentical items (2k outcomes), multidimensional types, private values, non-negative prices, and quasilinear preferences for the players with one relaxation — the players are subject to publicly-known budget constraints. We show that if it is publicly known that the players value the bundles more than the smaller of their budgets then the studied space includes one type of mechanism: autocratic mechanisms (a form of dictatorship). Furthermore, we prove that there are families of autocratic mechanisms that uniquely fulfill the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal. Interestingly the above basic properties are a weaker requirement than it may initially appear, as the property of Pareto optimality in our model of budget-constrained players and non-negative prices do not coincide with welfare maximization, i.e., efficiency as such is a much weaker requirement.

Compass enhanced ORRP for wireless sensor networks

Data routing in wireless sensor networks has attracted much research interest in recent years. Orthogonal Rendezvous Routing Protocol (ORRP) [1] was recently proposed and analyzed for use in wireless mesh networks. The protocol is based on a simple idea that two pairs of orthogonal lines in a plane intersect with a high probability and it utilizes the directional antennas for creating orthogonal routing paths. This protocol is appealing for wireless sensor networks as well. However wireless sensor networks differ from wireless mesh networks in many aspects, like the number of nodes in the network, many-to-one versus many-to-many communication, random node placement, and more. In this paper we analyze the suitability of ORRP for wireless sensor networks and propose a number of modifications, like equipping wireless sensor nodes with digital compass hardware. We then show that the proposed modifications improve reachability, reduce the average length of the path from a sensor to the base station and reduce the average number of nodes involved in an event forwarding.

Prosodic Plot of Dialogues: A Conceptual Framework to Trace Speakers' Role.

In this paper we present a proof-of-concept study which aims to model a conceptual framework to analyze structures of dialogues. We demonstrate our approach on a specific research question – how speaker’s role is realized along the dialogue? To this end, we use a unified set of Map Task dialogues that are unique in the sense that each speaker participated twice – once as a follower and once as a leader, with the same interlocutor playing the other role. This pairwise setting enables to compare prosodic differences in three facets: Role, Speaker, and Session. For this POC, we analyze a basic set of prosodic features: Talk proportions, pitch, and intensity. To create comparable methodological framework for dialogues, we created three plots of the three prosodic features, in ten equal sized intervals along the session. We used a simple distance measure between the resulting ten-dimensional vectors of each facet for each feature. The prosodic plots of these dialogues reveal the interactions and common behaviour across each facet, on the one hand, and allow to trace potential locations of extreme prosodic values, suggesting pivot points of each facet, on the other.

Automatic Speaker's Role Classification With a Bottom-up Acoustic Feature Selection

The objective of the current study is to automatically identify the role played by the speaker in a dialogue. By using machine learning procedures over acoustic feature, we wish to automatically trace the footprints of this information through the speech signal. The acoustic feature set was selected from a large statistic-based feature sets including 1,583 dimension features. The analysis is carried out on interactive dialogues of a Map Task setting. The paper first describes the methodology of choosing the 100 most effective attributes among the 1,583 features that were extracted, and then presents the classification results test of the same speaker in two different roles, and a gender-based classification. Results show an average of a 71% classification rate of the role the same speaker played, 65% for all women together and 65% for all men together.

Characterizing incentive compatible, Pareto optimal and sufficiently anonymous constrained combinatorial mechanisms – Two players case

We characterize the possibility space of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal combinatorial auctions in a model with two players and two nonidentical items. Our model has multidi- mensional types, private values, quasilinear preferences for the players with one relaxation - one of the players is subject to a publicly-known budget constraint. We show that the space includes two types of mechanisms: VCG and dictatorial mechanisms. Furthermore when it is publicly known that the budgeted player is not constrained by his budget, VCG uniquely fulfills the basic properties of deterministic, dominant-strategy incentive compatible, individually rational, and Pareto-optimal. When it is pub- licly known that the budgeted player is constrained on all bundles then only a dictatorial solution will fulfill the above properties. Moreover when it is publicly known that the budgeted player is constrained on the largest bundle there are preferences under which the VCG mechanism uniquely fulfills these properties.

Efficient Constrained Combinatorial Auctions

The seminal work by Green and Laffont [(1977) characterization of satisfactory mechanisms for the revelation of preferences for public goods, Econometrica 45, 427–438] shows that efficient mechanisms with Vickrey–Clarke–Groves prices satisfy the properties of dominant-strategy incentive compatible (DSIC) and individually rational in the quasilinear utilities model. Nevertheless in many real-world situations some players have a gap between their willingness to pay and their ability to pay, i.e., a budget. We show that once budgets are integrated into the model then Green and Laffont’s theorem ceases to apply. More specifically, we show that even if only a single player has budget constraints then there is no deterministic efficient mechanism that satisfies the individual rationality and DSIC properties. Furthermore, in a quasilinear utilities model with k nonidentical items and n players with multidimensional types, we characterize the sufficient and necessary conditions under which Green and Laffont’s theorem holds in the presence of budget-constrained players. Interestingly our characterization is similar in spirit to that of Maskin [(2000) Auctions, development and privatization: Efficient auctions with liquidity-constrained buyers, Eur. Econ. Rev. 44, 667–681] for Bayesian single-item constrained-efficiency auctions.