arXiv subjects

Moshe Babaioff

Publications and source records attributed to Moshe Babaioff.

At least 55 records · Page 3Linked to original sources

arXiv2018

Optimal Deterministic Mechanisms for an Additive Buyer

We study revenue maximization by deterministic mechanisms for the simplest case for which Myerson's characterization does not hold: a single seller selling two items, with independently distributed values, to a single additive buyer. We prove that optimal mechanisms are submodular and hence monotone. Furthermore, we show that in the IID case, optimal mechanisms are symmetric. Our characterizations are surprisingly non-trivial, and we show that they fail to extend in several natural ways, e.g. for correlated distributions or more than two items. In particular, this shows that the optimality of symmetric mechanisms does not follow from the symmetry of the IID distribution.

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arXiv2018

The Best of Both Worlds: Asymptotically Efficient Mechanisms with a Guarantee on the Expected Gains-From-Trade

The seminal impossibility result of Myerson and Satterthwaite (1983) states that for bilateral trade, there is no mechanism that is individually rational (IR), incentive compatible (IC), weakly budget balanced, and efficient. This has led follow-up work on two-sided trade settings to weaken the efficiency requirement and consider approximately efficient simple mechanisms, while still demanding the other properties. The current state-of-the-art of such mechanisms for two-sided markets can be categorized as giving one (but not both) of the following two types of approximation guarantees on the gains from trade: a constant ex-ante guarantee, measured with respect to the second-best efficiency benchmark, or an asymptotically optimal ex-post guarantee, measured with respect to the first-best efficiency benchmark. Here the second-best efficiency benchmark refers to the highest gains from trade attainable by any IR, IC and weakly budget balanced mechanism, while the first-best efficiency benchmark refers to the maximum gains from trade (attainable by the VCG mechanism, which is not weakly budget balanced). In this paper, we construct simple mechanisms for double-auction and matching markets that simultaneously achieve both types of guarantees: these are ex-post IR, Bayesian IC, and ex-post weakly budget balanced mechanisms that 1) ex-ante guarantee a constant fraction of the gains from trade of the second-best, and 2) ex-post guarantee a realization-dependent fraction of the gains from trade of the first-best, such that this realization-dependent fraction converges to 1 (full efficiency) as the market grows large.

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arXiv2017

Submultiplicative Glivenko-Cantelli and Uniform Convergence of Revenues

In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution. Our variant allows for tighter convergence bounds for extreme values of the CDF. We apply our bound in the context of revenue learning, which is a well-studied problem in economics and algorithmic game theory. We derive sample-complexity bounds on the uniform convergence rate of the empirical revenues to the true revenues, assuming a bound on the $k$th moment of the valuations, for any (possibly fractional) $k>1$. For uniform convergence in the limit, we give a complete characterization and a zero-one law: if the first moment of the valuations is finite, then uniform convergence almost surely occurs; conversely, if the first moment is infinite, then uniform convergence almost never occurs.

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arXiv2017

Selling Complementary Goods: Dynamics, Efficiency and Revenue

We consider a price competition between two sellers of perfect-complement goods. Each seller posts a price for the good it sells, but the demand is determined according to the sum of prices. This is a classic model by Cournot (1838), who showed that in this setting a monopoly that sells both goods is better for the society than two competing sellers. We show that non-trivial pure Nash equilibria always exist in this game. We also quantify Cournot's observation with respect to both the optimal welfare and the monopoly revenue. We then prove a series of mostly negative results regarding the convergence of best response dynamics to equilibria in such games.

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arXiv2017

ERA: A Framework for Economic Resource Allocation for the Cloud

Cloud computing has reached significant maturity from a systems perspective, but currently deployed solutions rely on rather basic economics mechanisms that yield suboptimal allocation of the costly hardware resources. In this paper we present Economic Resource Allocation (ERA), a complete framework for scheduling and pricing cloud resources, aimed at increasing the efficiency of cloud resources usage by allocating resources according to economic principles. The ERA architecture carefully abstracts the underlying cloud infrastructure, enabling the development of scheduling and pricing algorithms independently of the concrete lower-level cloud infrastructure and independently of its concerns. Specifically, ERA is designed as a flexible layer that can sit on top of any cloud system and interfaces with both the cloud resource manager and with the users who reserve resources to run their jobs. The jobs are scheduled based on prices that are dynamically calculated according to the predicted demand. Additionally, ERA provides a key internal API to pluggable algorithmic modules that include scheduling, pricing and demand prediction. We provide a proof-of-concept software and demonstrate the effectiveness of the architecture by testing ERA over both public and private cloud systems -- Azure Batch of Microsoft and Hadoop/YARN. A broader intent of our work is to foster collaborations between economics and system communities. To that end, we have developed a simulation platform via which economics and system experts can test their algorithmic implementations.

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arXiv2016

On Bitcoin and Red Balloons

Many large decentralized systems rely on information propagation to ensure their proper function. We examine a common scenario in which only participants that are aware of the information can compete for some reward, and thus informed participants have an incentive not to propagate information to others. One recent example in which such tension arises is the 2009 DARPA Network Challenge (finding red balloons). We focus on another prominent example: Bitcoin, a decentralized electronic currency system. Bitcoin represents a radical new approach to monetary systems. It has been getting a large amount of public attention over the last year, both in policy discussions and in the popular press. Its cryptographic fundamentals have largely held up even as its usage has become increasingly widespread. We find, however, that it exhibits a fundamental problem of a different nature, based on how its incentives are structured. We propose a modification to the protocol that can eliminate this problem. Bitcoin relies on a peer-to-peer network to track transactions that are performed with the currency. For this purpose, every transaction a node learns about should be transmitted to its neighbors in the network. The current implemented protocol provides an incentive to nodes to not broadcast transactions they are aware of. Our solution is to augment the protocol with a scheme that rewards information propagation. Since clones are easy to create in the Bitcoin system, an important feature of our scheme is Sybil-proofness. We show that our proposed scheme succeeds in setting the correct incentives, that it is Sybil-proof, and that it requires only a small payment overhead, all this is achieved with iterated elimination of dominated strategies. We complement this result by showing that there are no reward schemes in which information propagation and no self-cloning is a dominant strategy.

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arXiv2016

Networks of Complements

We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the pricing game between the sellers. We prove positive and negative results, both of "Price of Anarchy" and of "Price of Stability" type, for special families of graphs (paths, cycles) as well as more general ones (trees, graphs). We describe best-reply dynamics that converge to non-trivial equilibrium in several families of graphs, and we use these dynamics to prove the existence of approximately-efficient equilibria.

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arXiv2015

Truthful Mechanisms with Implicit Payment Computation

It is widely believed that computing payments needed to induce truthful bidding is somehow harder than simply computing the allocation. We show that the opposite is true: creating a randomized truthful mechanism is essentially as easy as a single call to a monotone allocation rule. Our main result is a general procedure to take a monotone allocation rule for a single-parameter domain and transform it (via a black-box reduction) into a randomized mechanism that is truthful in expectation and individually rational for every realization. The mechanism implements the same outcome as the original allocation rule with probability arbitrarily close to 1, and requires evaluating that allocation rule only once. We also provide an extension of this result to multi-parameter domains and cycle-monotone allocation rules, under mild star-convexity and non-negativity hypotheses on the type space and allocation rule, respectively. Because our reduction is simple, versatile, and general, it has many applications to mechanism design problems in which re-evaluating the allocation rule is either burdensome or informationally impossible. Applying our result to the multi-armed bandit problem, we obtain truthful randomized mechanisms whose regret matches the information-theoretic lower bound up to logarithmic factors, even though prior work showed this is impossible for truthful deterministic mechanisms. We also present applications to offline mechanism design, showing that randomization can circumvent a communication complexity lower bound for deterministic payments computation, and that it can also be used to create truthful shortest path auctions that approximate the welfare of the VCG allocation arbitrarily well, while having the same running time complexity as Dijkstra's algorithm.

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arXiv2015

Price Competition, Fluctuations, and Welfare Guarantees

In various markets where sellers compete in price, price oscillations are observed rather than convergence to equilibrium. Such fluctuations have been empirically observed in the retail market for gasoline, in airline pricing and in the online sale of consumer goods. Motivated by this, we study a model of price competition in which an equilibrium rarely exists. We seek to analyze the welfare, despite the nonexistence of an equilibrium, and present welfare guarantees as a function of the market power of the sellers. We first study best response dynamics in markets with sellers that provide a homogeneous good, and show that except for a modest number of initial rounds, the welfare is guaranteed to be high. We consider two variations: in the first the sellers have full information about the valuation of the buyer. Here we show that if there are $n$ items available across all sellers and $n_{\max}$ is the maximum number of items controlled by any given seller, the ratio of the optimal welfare to the achieved welfare will be at most $\log(\frac{n}{n-n_{\max}+1})+1$. As the market power of the largest seller diminishes, the welfare becomes closer to optimal. In the second variation we consider an extended model where sellers have uncertainty about the buyer's valuation. Here we similarly show that the welfare improves as the market power of the largest seller decreases, yet with a worse ratio of $\frac{n}{n-n_{\max}+1}$. The exponential gap in welfare between the two variations quantifies the value of accurately learning the buyer valuation. Finally, we show that extending our results to heterogeneous goods in general is not possible. Even for the simple class of $k$-additive valuations, there exists a setting where the welfare approximates the optimal welfare within any non-zero factor only for $O(1/s)$ fraction of the time, where $s$ is the number of sellers.

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arXiv2015

Mechanism Design with Strategic Mediators

We consider the problem of designing mechanisms that interact with strategic agents through strategic intermediaries (or mediators), and investigate the cost to society due to the mediators' strategic behavior. Selfish agents with private information are each associated with exactly one strategic mediator, and can interact with the mechanism exclusively through that mediator. Each mediator aims to optimize the combined utility of his agents, while the mechanism aims to optimize the combined utility of all agents. We focus on the problem of facility location on a metric induced by a publicly known tree. With non-strategic mediators, there is a dominant strategy mechanism that is optimal. We show that when both agents and mediators act strategically, there is no dominant strategy mechanism that achieves any approximation. We, thus, slightly relax the incentive constraints, and define the notion of a two-sided incentive compatible mechanism. We show that the $3$-competitive deterministic mechanism suggested by Procaccia and Tennenholtz (2013) and Dekel et al. (2010) for lines extends naturally to trees, and is still $3$-competitive as well as two-sided incentive compatible. This is essentially the best possible. We then show that by allowing randomization one can construct a $2$-competitive randomized mechanism that is two-sided incentive compatible, and this is also essentially tight. This result also closes a gap left in the work of Procaccia and Tennenholtz (2013) and Lu et al. (2009) for the simpler problem of designing strategy-proof mechanisms for weighted agents with no mediators on a line, while extending to the more general model of trees. We also investigate a further generalization of the above setting where there are multiple levels of mediators.

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arXiv2014

Mixed Strategies in Combinatorial Agency

In many multiagent domains a set of agents exert effort towards a joint outcome, yet the individual effort levels cannot be easily observed. A typical example for such a scenario is routing in communication networks, where the sender can only observe whether the packet reached its destination, but often has no information about the actions of the intermediate routers, which influences the final outcome. We study a setting where a principal needs to motivate a team of agents whose combination of hidden efforts stochastically determines an outcome. In a companion paper we devise and study a basic combinatorial agency model for this setting, where the principal is restricted to inducing a pure Nash equilibrium. Here we study various implications of this restriction. First, we show that, in contrast to the case of observable efforts, inducing a mixed-strategies equilibrium may be beneficial for the principal. Second, we present a sufficient condition for technologies for which no gain can be generated. Third, we bound the principals gain for various families of technologies. Finally, we study the robustness of mixed equilibria to coalitional deviations and the computational hardness of the optimal mixed equilibria.

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arXiv2014

Price Competition in Online Combinatorial Markets

We consider a single buyer with a combinatorial preference that would like to purchase related products and services from different vendors, where each vendor supplies exactly one product. We study the general case where subsets of products can be substitutes as well as complementary and analyze the game that is induced on the vendors, where a vendor's strategy is the price that he asks for his product. This model generalizes both Bertrand competition (where vendors are perfect substitutes) and Nash bargaining (where they are perfect complements), and captures a wide variety of scenarios that can appear in complex crowd sourcing or in automatic pricing of related products. We study the equilibria of such games and show that a pure efficient equilibrium always exists. In the case of submodular buyer preferences we fully characterize the set of pure Nash equilibria, essentially showing uniqueness. For the even more restricted "substitutes" buyer preferences we also prove uniqueness over {\em mixed} equilibria. Finally we begin the exploration of natural generalizations of our setting such as when services have costs, when there are multiple buyers or uncertainty about the the buyer's valuation, and when a single vendor supplies multiple products.

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arXiv2013

Dynamic Pricing with Limited Supply

We consider the problem of dynamic pricing with limited supply. A seller has $k$ identical items for sale and is facing $n$ potential buyers ("agents") that are arriving sequentially. Each agent is interested in buying one item. Each agent's value for an item is an IID sample from some fixed distribution with support $[0,1]$. The seller offers a take-it-or-leave-it price to each arriving agent (possibly different for different agents), and aims to maximize his expected revenue. We focus on "prior-independent" mechanisms -- ones that do not use any information about the distribution. They are desirable because knowing the distribution is unrealistic in many practical scenarios. We study how the revenue of such mechanisms compares to the revenue of the optimal offline mechanism that knows the distribution ("offline benchmark"). We present a prior-independent dynamic pricing mechanism whose revenue is at most $O((k \log n)^{2/3})$ less than the offline benchmark, for every distribution that is regular. In fact, this guarantee holds without *any* assumptions if the benchmark is relaxed to fixed-price mechanisms. Further, we prove a matching lower bound. The performance guarantee for the same mechanism can be improved to $O(\sqrt{k} \log n)$, with a distribution-dependent constant, if $k/n$ is sufficiently small. We show that, in the worst case over all demand distributions, this is essentially the best rate that can be obtained with a distribution-specific constant. On a technical level, we exploit the connection to multi-armed bandits (MAB). While dynamic pricing with unlimited supply can easily be seen as an MAB problem, the intuition behind MAB approaches breaks when applied to the setting with limited supply. Our high-level conceptual contribution is that even the limited supply setting can be fruitfully treated as a bandit problem.

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arXiv2013

Bertrand Networks

We study scenarios where multiple sellers of a homogeneous good compete on prices, where each seller can only sell to some subset of the buyers. Crucially, sellers cannot price-discriminate between buyers. We model the structure of the competition by a graph (or hyper-graph), with nodes representing the sellers and edges representing populations of buyers. We study equilibria in the game between the sellers, prove that they always exist, and present various structural, quantitative, and computational results about them. We also analyze the equilibria completely for a few cases. Many questions are left open.

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arXiv2013

On the Efficiency of the Walrasian Mechanism

Central results in economics guarantee the existence of efficient equilibria for various classes of markets. An underlying assumption in early work is that agents are price-takers, i.e., agents honestly report their true demand in response to prices. A line of research in economics, initiated by Hurwicz (1972), is devoted to understanding how such markets perform when agents are strategic about their demands. This is captured by the \emph{Walrasian Mechanism} that proceeds by collecting reported demands, finding clearing prices in the \emph{reported} market via an ascending price tâtonnement procedure, and returns the resulting allocation. Similar mechanisms are used, for example, in the daily opening of the New York Stock Exchange and the call market for copper and gold in London. In practice, it is commonly observed that agents in such markets reduce their demand leading to behaviors resembling bargaining and to inefficient outcomes. We ask how inefficient the equilibria can be. Our main result is that the welfare of every pure Nash equilibrium of the Walrasian mechanism is at least one quarter of the optimal welfare, when players have gross substitute valuations and do not overbid. Previous analysis of the Walrasian mechanism have resorted to large market assumptions to show convergence to efficiency in the limit. Our result shows that approximate efficiency is guaranteed regardless of the size of the market.

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arXiv2013

Characterizing Truthful Multi-Armed Bandit Mechanisms

We consider a multi-round auction setting motivated by pay-per-click auctions for Internet advertising. In each round the auctioneer selects an advertiser and shows her ad, which is then either clicked or not. An advertiser derives value from clicks; the value of a click is her private information. Initially, neither the auctioneer nor the advertisers have any information about the likelihood of clicks on the advertisements. The auctioneer's goal is to design a (dominant strategies) truthful mechanism that (approximately) maximizes the social welfare. If the advertisers bid their true private values, our problem is equivalent to the "multi-armed bandit problem", and thus can be viewed as a strategic version of the latter. In particular, for both problems the quality of an algorithm can be characterized by "regret", the difference in social welfare between the algorithm and the benchmark which always selects the same "best" advertisement. We investigate how the design of multi-armed bandit algorithms is affected by the restriction that the resulting mechanism must be truthful. We find that truthful mechanisms have certain strong structural properties -- essentially, they must separate exploration from exploitation -- and they incur much higher regret than the optimal multi-armed bandit algorithms. Moreover, we provide a truthful mechanism which (essentially) matches our lower bound on regret.

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arXiv2013

Multi-parameter Mechanisms with Implicit Payment Computation

In this paper we show that payment computation essentially does not present any obstacle in designing truthful mechanisms, even for multi-parameter domains, and even when we can only call the allocation rule once. We present a general reduction that takes any allocation rule which satisfies "cyclic monotonicity" (a known necessary and sufficient condition for truthfulness) and converts it to a truthful mechanism using a single call to the allocation rule, with arbitrarily small loss to the expected social welfare. A prominent example for a multi-parameter setting in which an allocation rule can only be called once arises in sponsored search auctions. These are multi-parameter domains when each advertiser has multiple possible ads he may display, each with a different value per click. Moreover, the mechanism typically does not have complete knowledge of the click-realization or the click-through rates (CTRs); it can only call the allocation rule a single time and observe the click information for ads that were presented. % are not known. On the negative side, we show that an allocation that is truthful for any realization essentially cannot depend on the bids, and hence cannot do better than random selection for one agent. We then consider a relaxed requirement of truthfulness, only in expectation over the CTRs. Even for that relaxed version, making any progress is challenging as standard techniques for construction of truthful mechanisms (as using VCG or an MIDR allocation rule) cannot be used in this setting. We design an allocation rule with non-trivial performance and directly prove it is cyclic-monotone, and thus it can be used to create a truthful mechanism using our general reduction.

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arXiv2012

Combinatorial Auctions with Restricted Complements

Complements between goods - where one good takes on added value in the presence of another - have been a thorn in the side of algorithmic mechanism designers. On the one hand, complements are common in the standard motivating applications for combinatorial auctions, like spectrum license auctions. On the other, welfare maximization in the presence of complements is notoriously difficult, and this intractability has stymied theoretical progress in the area. For example, there are no known positive results for combinatorial auctions in which bidder valuations are multi-parameter and non-complement-free, other than the relatively weak results known for general valuations. To make inroads on the problem of combinatorial auction design in the presence of complements, we propose a model for valuations with complements that is parameterized by the "size" of the complements. A valuation in our model is represented succinctly by a weighted hypergraph, where the size of the hyper-edges corresponds to degree of complementarity. Our model permits a variety of computationally efficient queries, and non-trivial welfare-maximization algorithms and mechanisms. We design the following polynomial-time approximation algorithms and truthful mechanisms for welfare maximization with bidders with hypergraph valuations. 1- For bidders whose valuations correspond to subgraphs of a known graph that is planar (or more generally, excludes a fixed minor), we give a truthful and (1+epsilon)-approximate mechanism. 2- We give a polynomial-time, r-approximation algorithm for welfare maximization with hypergraph-r valuations. Our algorithm randomly rounds a compact linear programming relaxation of the problem. 3- We design a different approximation algorithm and use it to give a polynomial-time, truthful-in-expectation mechanism that has an approximation factor of O(log^r m).

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