arXiv subjects

Moshe Tennenholtz

Publications and source records attributed to Moshe Tennenholtz.

At least 109 records · Page 6Linked to original sources

arXiv2013

Pay or Play

We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and an- other with a payoff dependent on others' selected actions. This is, arguably, the simplest setting that models selection among certain and uncertain outcomes in a multi-agent system. We study the properties of equilibria in such games from both a game-theoretic perspective and a computational perspective. Our main positive result establishes the existence of a semi-strong equilibrium in every such game. We show that although simple, pay of play games contain a large variety of well-studied environments, e.g., vaccination games. We discuss the interesting implications of our results for these environments.

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arXiv2013

Equilibrium in Labor Markets with Few Firms

We study competition between firms in labor markets, following a combinatorial model suggested by Kelso and Crawford [1982]. In this model, each firm is trying to recruit workers by offering a higher salary than its competitors, and its production function defines the utility generated from any actual set of recruited workers. We define two natural classes of production functions for firms, where the first one is based on additive capacities (weights), and the second on the influence of workers in a social network. We then analyze the existence of pure subgame perfect equilibrium (PSPE) in the labor market and its properties. While neither class holds the gross substitutes condition, we show that in both classes the existence of PSPE is guaranteed under certain restrictions, and in particular when there are only two competing firms. As a corollary, there exists a Walrasian equilibrium in a corresponding combinatorial auction, where bidders' valuation functions belong to these classes. While a PSPE may not exist when there are more than two firms, we perform an empirical study of equilibrium outcomes for the case of weight-based games with three firms, which extend our analytical results. We then show that stability can in some cases be extended to coalitional stability, and study the distribution of profit between firms and their workers in weight-based games.

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arXiv2013

On Stable Multi-Agent Behavior in Face of Uncertainty

A stable joint plan should guarantee the achievement of a designer's goal in a multi-agent environment, while ensuring that deviations from the prescribed plan would be detected. We present a computational framework where stable joint plans can be studied, as well as several basic results about the representation, verification and synthesis of stable joint plans.

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arXiv2012

Mechanism Design with Execution Uncertainty

We introduce the notion of fault tolerant mechanism design, which extends the standard game theoretic framework of mechanism design to allow for uncertainty about execution. Specifically, we define the problem of task allocation in which the private information of the agents is not only their costs to attempt the tasks, but also their probabilities of failure. For several different instances of this setting we present technical results, including positive ones in the form of mechanisms that are incentive compatible, individually rational and efficient, and negative ones in the form of impossibility theorems.

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arXiv2012

Collusion in Unrepeated, First-Price Auctions with an Uncertain Number of Participants

We consider the question of whether collusion among bidders (a "bidding ring") can be supported in equilibrium of unrepeated first-price auctions. Unlike previous work on the topic such as that by McAfee and McMillan [1992] and Marshall and Marx [2007], we do not assume that non-colluding agents have perfect knowledge about the number of colluding agents whose bids are suppressed by the bidding ring, and indeed even allow for the existence of multiple cartels. Furthermore, while we treat the association of bidders with bidding rings as exogenous, we allow bidders to make strategic decisions about whether to join bidding rings when invited. We identify a bidding ring protocol that results in an efficient allocation in Bayes{Nash equilibrium, under which non-colluding agents bid straightforwardly, and colluding agents join bidding rings when invited and truthfully declare their valuations to the ring center. We show that bidding rings benefit ring centers and all agents, both members and non-members of bidding rings, at the auctioneer's expense. The techniques we introduce in this paper may also be useful for reasoning about other problems in which agents have asymmetric information about a setting.

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arXiv2012

Reputation Systems: An Axiomatic Approach

Reasoning about agent preferences on a set of alternatives, and the aggregation of such preferences into some social ranking is a fundamental issue in reasoning about uncertainty and multi-agent systems. When the set of agents and the set of alternatives coincide, we get the so-called reputation systems setting. Famous types of reputation systems include page ranking in the context of search engines and traders ranking in the context of e-commerce. In this paper we present the first axiomatic study of reputation systems. We present three basic postulates that the desired/aggregated social ranking should satisfy and prove an impossibility theorem showing that no appropriate social ranking, satisfying all requirements, exists. Then we show that by relaxing any of these requirements an appropriate social ranking can be found. We first study reputation systems with (only) positive feedbacks. This setting refers to systems where agents' votes are interpreted as indications for the importance of other agents, as is the case in page ranking. Following this, we discuss the case of negative feedbacks, a most common situation in e-commerce settings, where traders may complain about the behavior of others. Finally, we discuss the case where both positive and negative feedbacks are available.

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arXiv2012

Sequential Information Elicitation in Multi-Agent Systems

We introduce the study of sequential information elicitation in strategic multi-agent systems. In an information elicitation setup a center attempts to compute the value of a function based on private information (a-k-a secrets) accessible to a set of agents. We consider the classical multi-party computation setup where each agent is interested in knowing the result of the function. However, in our setting each agent is strategic,and since acquiring information is costly, an agent may be tempted not spending the efforts of obtaining the information, free-riding on other agents' computations. A mechanism which elicits agents' secrets and performs the desired computation defines a game. A mechanism is 'appropriate' if there exists an equilibrium in which it is able to elicit (sufficiently many) agents' secrets and perform the computation, for all possible secret vectors.We characterize a general efficient procedure for determining an appropriate mechanism, if such mechanism exists. Moreover, we also address the existence problem, providing a polynomial algorithm for verifying the existence of an appropriate mechanism.

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arXiv2012

On the Value of Correlation

Correlated equilibrium (Aumann, 1974) generalizes Nash equilibrium to allow correlation devices. Aumann showed an example of a game, and of a correlated equilibrium in this game, in which the agents' surplus (expected sum of payo s) is greater than their surplus in all mixed-strategy equilibria. Following the idea initiated by the price of anarchy literature (Koutsoupias & Papadimitriou, 1999;Papadimitriou, 2001) this suggests the study of two major measures for the value of correlation in a game with non-negative payoffs: 1. The ratio between the maximal surplus obtained in a correlated equilibrium to the maximal surplus obtained in a mixed-strategy equilibrium. We refer to this ratio as the mediation value. 2. The ratio between the maximal surplus to the maximal surplus obtained in a correlated equilibrium. We refer to this ratio as the enforcement value. In this work we initiate the study of the mediation and enforcement values, providing several general results on the value of correlation as captured by these concepts. We also present a set of results for the more specialized case of congestion games (Rosenthal,1973), a class of games that received a lot of attention in the recent literature.

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arXiv2012

Robust Learning Equilibrium

We introduce robust learning equilibrium. The idea of learning equilibrium is that learning algorithms in multi-agent systems should themselves be in equilibrium rather than only lead to equilibrium. That is, learning equilibrium is immune to strategic deviations: Every agent is better off using its prescribed learning algorithm, if all other agents follow their algorithms, regardless of the unknown state of the environment. However, a learning equilibrium may not be immune to non strategic mistakes. For example, if for a certain period of time there is a failure in the monitoring devices (e.g., the correct input does not reach the agents), then it may not be in equilibrium to follow the algorithm after the devices are corrected. A robust learning equilibrium is immune also to such non-strategic mistakes. The existence of (robust) learning equilibrium is especially challenging when the monitoring devices are 'weak'. That is, the information available to each agent at each stage is limited. We initiate a study of robust learning equilibrium with general monitoring structure and apply it to the context of auctions. We prove the existence of robust learning equilibrium in repeated first-price auctions, and discuss its properties.

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arXiv2012

Signaling Schemes for Revenue Maximization

Signaling is an important topic in the study of asymmetric information in economic settings. In particular, the transparency of information available to a seller in an auction setting is a question of major interest. We introduce the study of signaling when conducting a second price auction of a probabilistic good whose actual instantiation is known to the auctioneer but not to the bidders. This framework can be used to model impressions selling in display advertising. We study the problem of computing a signaling scheme that maximizes the auctioneer's revenue in a Bayesian setting. While the general case is proved to be computationally hard, several cases of interest are shown to be polynomially solvable. In addition, we establish a tight bound on the minimum number of signals required to implement an optimal signaling scheme and show that at least half of the maximum social welfare can be preserved within such a scheme.

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arXiv2012

Signalling Competition and Social Welfare (Working Paper)

We consider an environment where sellers compete over buyers. All sellers are a-priori identical and strategically signal buyers about the product they sell. In a setting motivated by on-line advertising in display ad exchanges, where firms use second price auctions, a firm's strategy is a decision about its signaling scheme for a stream of goods (e.g. user impressions), and a buyer's strategy is a selection among the firms. In this setting, a single seller will typically provide partial information and consequently a product may be allocated inefficiently. Intuitively, competition among sellers may induce sellers to provide more information in order to attract buyers and thus increase efficiency. Surprisingly, we show that such a competition among firms may yield significant loss in consumers' social welfare with respect to the monopolistic setting. Although we also show that in some cases the competitive setting yields gain in social welfare, we provide a tight bound on that gain, which is shown to be small in respect to the above possible loss. Our model is tightly connected with the literature on bundling in auctions.

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arXiv2012

Solving Cooperative Reliability Games

Cooperative games model the allocation of profit from joint actions, following considerations such as stability and fairness. We propose the reliability extension of such games, where agents may fail to participate in the game. In the reliability extension, each agent only "survives" with a certain probability, and a coalition's value is the probability that its surviving members would be a winning coalition in the base game. We study prominent solution concepts in such games, showing how to approximate the Shapley value and how to compute the core in games with few agent types. We also show that applying the reliability extension may stabilize the game, making the core non-empty even when the base game has an empty core.

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arXiv2012

Stability Scores: Measuring Coalitional Stability

We introduce a measure for the level of stability against coalitional deviations, called \emph{stability scores}, which generalizes widely used notions of stability in non-cooperative games. We use the proposed measure to compare various Nash equilibria in congestion games, and to quantify the effect of game parameters on coalitional stability. For our main results, we apply stability scores to analyze and compare the Generalized Second Price (GSP) and Vickrey-Clarke-Groves (VCG) ad auctions. We show that while a central result of the ad auctions literature is that the GSP and VCG auctions implement the same outcome in one of the equilibria of GSP, the GSP outcome is far more stable. Finally, a modified version of VCG is introduced, which is group strategy-proof, and thereby achieves the highest possible stability score.

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arXiv2011

Approximately Optimal Mechanism Design via Differential Privacy

In this paper we study the implementation challenge in an abstract interdependent values model and an arbitrary objective function. We design a mechanism that allows for approximate optimal implementation of insensitive objective functions in ex-post Nash equilibrium. If, furthermore, values are private then the same mechanism is strategy proof. We cast our results onto two specific models: pricing and facility location. The mechanism we design is optimal up to an additive factor of the order of magnitude of one over the square root of the number of agents and involves no utility transfers. Underlying our mechanism is a lottery between two auxiliary mechanisms: with high probability we actuate a mechanism that reduces players' influence on the choice of the social alternative, while choosing the optimal outcome with high probability. This is where the recent notion of differential privacy is employed. With the complementary probability we actuate a mechanism that is typically far from optimal but is incentive compatible. The joint mechanism inherits the desired properties from both.

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arXiv2011

Mechanism design with uncertain inputs (to err is human, to forgive divine)

We consider a task of scheduling with a common deadline on a single machine. Every player reports to a scheduler the length of his job and the scheduler needs to finish as many jobs as possible by the deadline. For this simple problem, there is a truthful mechanism that achieves maximum welfare in dominant strategies. The new aspect of our work is that in our setting players are uncertain about their own job lengths, and hence are incapable of providing truthful reports (in the strict sense of the word). For a probabilistic model for uncertainty our main results are as follows. 1) Even with relatively little uncertainty, no mechanism can guarantee a constant fraction of the maximum welfare. 2) To remedy this situation, we introduce a new measure of economic efficiency, based on a notion of a {\em fair share} of a player, and design mechanisms that are $Ω(1)$-fair. In addition to its intrinsic appeal, our notion of fairness implies good approximation of maximum welfare in several cases of interest. 3) In our mechanisms the machine is sometimes left idle even though there are jobs that want to use it. We show that this unfavorable aspect is unavoidable, unless one gives up other favorable aspects (e.g., give up $Ω(1)$-fairness). We also consider a qualitative approach to uncertainty as an alternative to the probabilistic quantitative model. In the qualitative approach we break away from solution concepts such as dominant strategies (they are no longer well defined), and instead suggest an axiomatic approach, which amounts to listing desirable properties for mechanisms. We provide a mechanism that satisfies these properties.

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arXiv2011

Dueling Algorithms

We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two players, whose only goal is to outperform the opponent. Such games are typically exponentially large zero-sum games, but they often have a rich combinatorial structure. We provide general techniques by which such structure can be leveraged to find minmax-optimal and approximate minmax-optimal strategies. We give examples of ranking, hiring, compression, and binary search duels, among others. We give bounds on how often one can beat the classic optimization algorithms in such duels.

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arXiv2009

Sum of Us: Strategyproof Selection from the Selectors

We consider directed graphs over a set of n agents, where an edge (i,j) is taken to mean that agent i supports or trusts agent j. Given such a graph and an integer k\leq n, we wish to select a subset of k agents that maximizes the sum of indegrees, i.e., a subset of k most popular or most trusted agents. At the same time we assume that each individual agent is only interested in being selected, and may misreport its outgoing edges to this end. This problem formulation captures realistic scenarios where agents choose among themselves, which can be found in the context of Internet search, social networks like Twitter, or reputation systems like Epinions. Our goal is to design mechanisms without payments that map each graph to a k-subset of agents to be selected and satisfy the following two constraints: strategyproofness, i.e., agents cannot benefit from misreporting their outgoing edges, and approximate optimality, i.e., the sum of indegrees of the selected subset of agents is always close to optimal. Our first main result is a surprising impossibility: for k \in {1,...,n-1}, no deterministic strategyproof mechanism can provide a finite approximation ratio. Our second main result is a randomized strategyproof mechanism with an approximation ratio that is bounded from above by four for any value of k, and approaches one as k grows.

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arXiv2009

Strategyproof Approximation Mechanisms for Location on Networks

We consider the problem of locating a facility on a network, represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to the location of the facility. Specifically, we are interested in social choice mechanisms that do not utilize payments. We wish to design mechanisms that are strategyproof, in the sense that agents can never benefit by lying, or, even better, group strategyproof, in the sense that a coalition of agents cannot all benefit by lying. At the same time, our mechanisms must provide a small approximation ratio with respect to one of two optimization targets: the social cost or the maximum cost. We give an almost complete characterization of the feasible truthful approximation ratio under both target functions, deterministic and randomized mechanisms, and with respect to different network topologies. Our main results are: We show that a simple randomized mechanism is group strategyproof and gives a (2-2/n)-approximation for the social cost, where n is the number of agents, when the network is a circle (known as a ring in the case of computer networks); we design a novel "hybrid" strategyproof randomized mechanism that provides a tight approximation ratio of 3/2 for the maximum cost when the network is a circle; and we show that no randomized SP mechanism can provide an approximation ratio better than 2-o(1) to the maximum cost even when the network is a tree, thereby matching a trivial upper bound of two.

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