Rica Gonen

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.

Incentive Compatible Mulit-Unit Combinatorial Auctions: A Primal Dual Approach

We study multi-unit combinatorial auctions with multi-minded buyers. We provide two deterministic, efficient maximizing, incentive compatible mechanisms that improve upon the known algorithms for the problem (Bartal et al., Proceedings of the 9th Conference on Theoretical Aspects of Rationality and Knowledge TARK IX, pp.xa072–87, 2003). The first mechanism is an online mechanism for a setting in which buyers arrive one-by-one in an online fashion. We then design an offline mechanism with better performance guarantees based on the online mechanism. We complement the results by lower bounds that show that the performance of our mechanisms is close to optimal. The results are based on an online primal-dual approach that was used extensively recently and reveals the underlying structure of the problem.

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.

Removal and Threshold Pricing: Truthful Two-Sided Markets with Multi-dimensional Participants

We consider mechanisms for markets that are two-sided and have agents with multi-dimensional strategic spaces on at least one side. The agents of the market are strategic and act to optimize their own utilities, while the mechanism designer aims to optimize a social goal, i.e., the gain from trade. We focus on one example of this setting motivated by a foreseeable privacy-aware future form of online advertising.

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.

Opinion Diffusion and Campaigning on Society Graphs

We study the effects of campaigning, where the society is partitioned into voter clusters and a diffusion process propagates opinions in a network connecting the clusters. Our model is very powerful and can incorporate many campaigning actions, various partitions of the society into clusters, and very general diffusion processes. Perhaps surprisingly, we show that computing the cheapest campaign for rigging a given election can usually be done efficiently, even with arbitrarily-many voters. Moreover, we report on certain computational simulations.

Multi-sided Advertising Markets: Dynamic Mechanisms and Incremental User Compensations

Online advertising has motivated companies to collect vast amounts of information about users, which increasingly creates privacy concerns. One way to answer these concerns is by enabling end users to choose which aspects of their private information can be collected. Based on principles suggested by Feldman and Gonen (2018), we introduce a new online advertising market model which uses information brokers to give users such control. Unlike Feldman and Gonen (2018), our model is dynamic and involves multi-sided markets where all participating sides are strategic. We describe a mechanism for this model which is theoretically guaranteed to (approximately) maximize the gain from trade, avoid a budget deficit and incentivize truthfulness and voluntary participation. As far as we know, this is the first known dynamic mechanism for a multi-sided market having these properties.

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.