Yonatan Aumann

Bar Ilan University, Gan, Tel Aviv, Israel

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Publications (105)43.27 Total impact

  • Yonatan Aumann · Yair Dombb · Avinatan Hassidim

    No preview · Article · Dec 2015
  • Orit Arzi · Yonatan Aumann · Yair Dombb
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    ABSTRACT: We consider the problem of fairly dividing a heterogeneous good (a.k.a. “cake”) between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here we show that, in some cases, leaving some of the cake unallocated, and fairly dividing only the remainder of the cake may be socially preferable to any fair division of the entire cake. We study this phenomenon, providing asymptotically-tight bounds on the social improvement achievable by such partial divisions.
    No preview · Article · Dec 2015 · Social Choice and Welfare
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    DESCRIPTION: Abstract We consider the problem of fairly dividing a two-dimensional heterogeneous good, such as land or ad space in print and electronic media, among several agents with different utilities. Classic cake-cutting procedures either allocate each agent a collection of disconnected pieces, or assume that the cake is a one-dimensional interval. In practice, however, the two-dimensional shape of the allotted pieces may be of crucial importance. In particular, when building a house or designing an advertisement, squares are more usable than long and narrow rectangles. We thus introduce and study the problem of fair two-dimensional division wherein the allotted pieces must be of some restricted two-dimensional geometric shape(s). Adding this geometric constraint re-opens most questions and challenges related to cake-cutting. Indeed, even the most elementary fairness criterion - proportionality - can no longer be guaranteed. In this paper we thus examine the level of proportionality that can be guaranteed, providing both impossibility results (for proportionality that cannot be guaranteed) and division procedures (for proportionality that can be guaranteed). We consider cakes and pieces of various shapes, focusing primarily on shapes with a balanced aspect ratio such as squares.
    No preview · Research · Oct 2015
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    Erel Segal-Halevi · Avinatan Hassidim · Yonatan Aumann

    Full-text · Dataset · Aug 2015
  • Erel Segal-Halevi · Avinatan Hassidim · Yonatan Aumann
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    ABSTRACT: We consider the classic problem of envy-free division of a heterogeneous good (aka the cake) among multiple agents. It is well known that if each agent must receive a contiguous piece then there is no finite protocol for the problem, whenever there are 3 or more agents. This impossibility result, however, assumes that the entire cake must be allocated. In this paper we study the problem in a setting where the protocol may leave some of the cake un-allocated, as long as each agent obtains at least some positive value (according to its valuation). We prove that this version of the problem is solvable in a bounded time. For the case of 3 agents we provide a finite and bounded-time protocol that guarantees each agent a share with value at least 1/3, which is the most that can be guaranteed.
    No preview · Conference Paper · May 2015
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    Erel Segal-Halevi · Avinatan Hassidim · Yonatan Aumann
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    ABSTRACT: We consider the problem of fair division of a two dimensional heterogeneous good among several agents. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols either consider a one-dimensional resource, or allocate each agent several disconnected pieces. In practice, however, the two dimensional shape of the allotted piece is of crucial importance in many applications, e.g., squares or bounded aspect-ratio rectangles are most useful for building houses as well as advertisements. We thus introduce and study the problem of envy-free two-dimensional division wherein the utility of the agents depends on the geometric shape of the allocated pieces (as well as the location and size). In addition to envy-freeness, we require that the fraction allocated to each agent be at least a certain constant that depends only on the shape of the cake and the number of agents. We focus on the case where the allotted pieces must be square and the cakes are either squares or the unbounded plane. We provide algorithms for the problem for settings with two and three agents.
    Full-text · Conference Paper · Jan 2015
  • David Sarne · Yonatan Aumann
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    ABSTRACT: We consider settings were agents are faced with several possible opportunities and need to choose one. Each opportunity may offer a different utility to the agent, and determining this utility may consume resources. The underlying costly exploration problem is termed “economic search”, though its essence is different from the traditional search notion in artificial intelligence (e.g. BFS, IDDFA, and A*), as there is no underlying combinatorial structure to the opportunities. We study the effects that search costs can have on individual and aggregate utility in distributed multi-agent economic-search settings. Traditionally, in such setting, search costs are regarded as a market inefficiency, and, as such, as something to be avoided or reduced to a minimum. We show, in contrast, that in many search settings, the introduction of search costs can actually improve the aggregate social welfare, or even the expected utility of each and every individual agent.We note that the proceeds from the search costs are assumed to be wasted, with no one directly benefiting from them. We demonstrate the benefits of search costs in both one-sided and two-sided search settings, using standard, classical models from economic-search theory. For the designers of multiagent systems, the results imply that deliberate (and potentially artificial) increase of search costs should be considered as possible means to improving the system’s overall performance.
    No preview · Article · Nov 2014 · Annals of Mathematics and Artificial Intelligence
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    Erel Segal-Halevi · Avinatan Hassidim · Yonatan Aumann
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    ABSTRACT: We consider the problem of fairly dividing a two dimensional heterogeneous good among multiple players. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols primarily consider a one-dimensional resource, or allocate each player multiple infinitesimally small "pieces". In practice, however, the two dimensional \emph{shape} of the allotted piece is of crucial importance in many applications (e.g. squares or bounded aspect-ratio rectangles are most useful for building houses, as well as advertisements). We thus introduce and study the problem of fair two-dimensional division wherein the allotted plots must be of some restricted two-dimensional geometric shape(s). Adding this geometric constraint re-opens most questions and challenges related to cake-cutting. Indeed, even the elementary \emph{proportionality} fairness criteria can no longer be guaranteed in all cases. In this paper we thus examine the \emph{level} of proportionality that \emph{can} be guaranteed, providing both impossibility results (for proportionality that cannot be guaranteed), and algorithmic constructions (for proportionality that can be guaranteed). We focus primarily on the case when the cake is a rectilinear polygon and the allotted plots must be squares or bounded aspect-ratio rectangles.
    Full-text · Article · Sep 2014
  • Amihood Amir · Yonatan Aumann · Piotr Indyk · Avivit Levy · Ely Porat
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    ABSTRACT: Recently, a new pattern matching paradigm was proposed, pattern matching with address errors. In this paradigm approximate string matching problems are studied, where the content is unaltered and only the locations of the different entries may change. Specifically, a broad class of problems was defined—the class of rearrangement errors. In this type of error the pattern is transformed through a sequence of rearrangement operations, each with an associated cost. The natural ℓ[subscript 1] and ℓ[subscript 2] rearrangement systems were considered. The best algorithm presented for general patterns, that may have repeating symbols, is O(nm). In this paper, we show that the problem can be approximated in linear time for general patterns! Another natural rearrangement system is considered in this paper—the ℓ[subscript ∞] rearrangement distance. For this new rearrangement system efficient exact solutions for different variants of the problem are provided, as well as a faster approximation.
    No preview · Article · May 2014
  • Igor Rochlin · Yonatan Aumann · David Sarne · Luba Golosman
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    ABSTRACT: We consider team-work settings where individual agents incur costs on behalf of the team. In such settings it is frequently the custom to reimburse agents for the costs they incur (at least in part) in order to promote fairness. We show, however, that when agents are self-interested such reimbursement can result in degradation in efficiency - at times severe degradation. We thus study the relationship between efficiency and fairness in such settings, distinguishing between ex-ante and ex-post fairness. First, we analyze reimbursement policies that reimburse solely based on purchase receipts (as is customary), and show that with such policies the degradation in both efficiency and fairness can be unbounded. We thus introduce two other families of reimbursement policies. The first family guarantees optimal efficiency and ex-ante fairness, but not ex-post fairness. The second family improves (at times) on ex-post fairness, but at the expense of efficiency, thus providing a tradeoff between the two.
    No preview · Conference Paper · May 2014
  • Y. Aumann · Y. Dombb · A. Hassidim
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    ABSTRACT: We consider the problem of auctioning a one-dimensional continuously-divisible heterogeneous good (a.k.a. "the cake") among multiple agents. Applications include auctioning of time intervals, e.g. auctioning time for usage of a shared device, auctioning TV commercial slots, and more. Different agents may have different valuations for the different possible intervals, and the goal is to maximize the aggregate utility. Agents are self-interested and may misrepresent their true valuation functions, if this benefits them. Thus, we seek auctions that are truthful. Considering the case that each agent may obtain a single interval, the challenge is twofold, as we need to determine both where to slice the interval, and who gets which slice. The associated computational problem is NP-hard even under very restrictive assumptions. We consider two settings: discrete and continuous. In the discrete setting we are given a sequence of m indivisible elements (e1,⋯, em), and the auction must allocate each agent a consecutive subsequence of the elements. For this setting we provide a truthful auctioning mechanism that approximates the optimal welfare to within a log m factor. The mechanism works for arbitrary monotone valuations. In the continuous setting we are given a continuous, infinitely divisible interval, and the auction must allocate each agent a sub-interval. The agents' valuations are non-atomic measures on the interval. For this setting we provide a truthful auctioning mechanism that approximates the optimal welfare to within a O(logn) factor (where n is the number of agents). Additionally, we provide a truthful 2-approximation mechanism for the case that all slices must be of some fixed size. Copyright © 2014, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.
    No preview · Article · Jan 2014
  • Amos Azaria · Yonatan Aumann · Sarit Kraus
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    ABSTRACT: Crowdsourcing applications frequently employ many individual workers, each performing a small amount of work. In such settings, individually determining the reward for each assignment and worker may seem economically beneficial, but is inapplicable if manually performed. We thus consider the problem of designing automated agents for automatic reward determination and negotiation in such settings. We formally describe this problem and show that it is NP-hard. We therefore present two automated agents for the problem, based on two different models of human behavior. The first, the Reservation Price Based Agent (RPBA), is based on the concept of a RP, and the second, the No Bargaining Agent (NBA) which tries to avoid any negotiation. The performance of the agents is tested in extensive experiments with real human subjects, where both NBA and RPBA outperform strategies developed by human experts.
    No preview · Article · Nov 2013 · Autonomous Agents and Multi-Agent Systems
  • Noam Hazon · Yonatan Aumann · Sarit Kraus · David Sarne
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    ABSTRACT: This paper considers the problem of an agent or a team of agents searching for a resource or tangible good in a physical environment, where the resource or good may possibly be obtained at one of several locations. The cost of acquiring the resource or good at a given location is uncertain (a priori), and the agents can observe the true cost only when physically arriving at this location. Sample applications include agents in exploration and patrol missions (e.g., an agent seeking to find the best location to deploy sensing equipment along its path). The uniqueness of these settings is in that the cost of observing a new location is determined by distance from the current one, impacting the consideration for the optimal search order. Although this model captures many real world scenarios, it has not been investigated so far.
    No preview · Article · Mar 2013 · Artificial Intelligence
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    Amos Azaria · David Sarner · Yonatan Aumann
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    ABSTRACT: In this paper we study distributed agent matching in environments characterized by costly exploration, where each agent's utility from forming a partnership is influenced by both the maximum and the minimum among the two agent's competence. This kind of utility function is somehow more applicable, compared to the one used in related work that takes the utility to be either the type of the agent partner or "standard" functions such as average or multiplication of the two types. The use of the hybrid min-max utility function is favorable whenever the performance of the agents forming a partnership is principally affected by the most (or least) competent among the two. This paper supplies a cohesive analysis for the min-max case, proving the equilibrium structure for the different min-max linear combination that may be used. We show that in any case that an agent sets its acceptance threshold below its own type it is guaranteed that any agent with a type between this threshold and its own will accept it (the agent) as a partner as well. This result substantially facilitates the calculation of equilibrium for such settings, e.g., when the set of types is finite.
    Preview · Conference Paper · Dec 2012
  • David Sarne · Yonatan Aumann
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    ABSTRACT: Humans and software agents alike spend considerable time and effort in searching. Search enables finding the things that better fit and agent's goals. But search can also be a costly process. Search costs can either come in the form of direct monetary payments, or in the form of time and resources spent. In general, the searcher must balance between the benefits provided by longer and broader search, on the one hand, and the associated increased cost, on the other.
    No preview · Conference Paper · Jun 2012
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    Yonatan Aumann · Yair Dombb · Avinatan Hassidim
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    ABSTRACT: We consider a setting in which a single divisible good ("cake") needs to be divided between n players, each with a possibly di?fferent valuation function over pieces of the cake. For this setting, we address the problem of ?finding divisions that maximize the social welfare, focusing on divisions where each player needs to get one contiguous piece of the cake. We show that for both the utilitarian and the egalitarian social welfare functions it is NP-hard to find the optimal division. For the utilitarian welfare, we provide a constant factor approximation algorithm, and prove that no FPTAS is possible unless P=NP. For egalitarian welfare, we prove that it is NP-hard to approximate the optimum to any factor smaller than 2. For the case where the number of players is small, we provide an FPT (fixed parameter tractable) FPTAS for both the utilitarian and the egalitarian welfare objectives.
    Preview · Article · May 2012
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    ABSTRACT: We introduce a generalization of interval graphs, which we call dotted interval graphs (DIG). A dotted interval graph is an intersection graph of arithmetic progressions (=dotted intervals). Coloring of dotted intervals graphs naturally arises in the context of high throughput genotyping. We study the properties of dotted interval graphs, with a focus on coloring. We show that any graph is a DIG but that DIG d graphs, i.e. DIGs in which the arithmetic progressions have a jump of at most d, form a strict hierarchy. We show that coloring DIG d graphs is NP-complete even for d = 2. For any fixed d, we provide a 7 8 d approximation for the coloring of DIG d graphs.
    Full-text · Article · Apr 2012 · ACM Transactions on Algorithms
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    Amos Azaria · Yonatan Aumann · Sarit Kraus
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    ABSTRACT: We consider the problem of designing automated strategies for interactions with human subjects, where the humans must be rewarded for performing certain tasks of interest. We fo-cus on settings where there is a single task that must be per-formed many times by different humans (e.g. answering a questionnaire), and the humans require a fee for perform-ing the task. In such settings, our objective is to minimize the average cost for effectuating the completion of the task. We present two automated strategies for designing efficient agents for the problem, based on two different models of hu-man behavior. The first, the Reservation Price Based Agent (RPBA), is based on the concept of a reservation price, and the second, the No Bargaining Agent (NBA), uses principles from behavioral science. The performance of the agents has been tested in extensive experiments with real human sub-jects, where NBA outperforms both RPBA and strategies de-veloped by human experts.
    Full-text · Article · Jan 2012
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    David Sarne · Yonatan Aumann
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    ABSTRACT: In this paper we study the benefits of search costs in distributed multi-agent systems (MAS). These costs, often associated with obtaining, pro-cessing and evaluating information relating to other agents in the environment, can be either monetary or manifested in some tax on the agent's resources. Tra-ditionally, such costs are considered as market inefficiency, and, as such, aimed to be reduced to the minimum. Here we show, in contrast, that in many MAS settings the introduction of search costs can actually improve market perfor-mance. This is demonstrated in three different settings. First we consider one-sided and two-sided (equilibrium-driven) search applications. In both settings we show that, while search costs may decrease the individual agents' outcomes, the overall market throughput may actually improve with the introduction of such costs. Next, we demonstrate a setting where, somewhat paradoxically, the introduction of search costs improves both the overall market throughput and the utility of each and every individual agent. We stress that we assume that the proceeds from the search costs are wasted, with no one directly benefiting from them. The importance of the results is for the design of MAS systems, where in many cases one should consider deliberately increasing (potentially artificially) the search friction to some desired level in order to improve the system's performance.
    Preview · Article · Jan 2012 · Lecture Notes in Business Information Processing
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    Orit Arzi · Yonatan Aumann · Yair Dombb
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    ABSTRACT: We consider the problem of fairly dividing a heterogeneous cake between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here, we show that in some cases, discarding some of the cake and fairly dividing only the remainder may be socially preferable to any fair division of the entire cake. We study this phenomenon, providing asymptotically-tight bounds on the social improvement achievable by such discarding.
    Preview · Conference Paper · Oct 2011

Publication Stats

2k Citations
43.27 Total Impact Points

Institutions

  • 1970-2014
    • Bar Ilan University
      • Department of Computer Science
      Gan, Tel Aviv, Israel
  • 1998
    • Harvard University
      Cambridge, Massachusetts, United States
  • 1990-1994
    • Hebrew University of Jerusalem
      • • Rachel and Selim Benin School of Computer Science and Engineering
      • • Otto Loewi Minerva Center for Neurobiology
      Yerushalayim, Jerusalem District, Israel
  • 1993
    • Weizmann Institute of Science
      Israel