[Show description][Hide description] 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.
[Show abstract][Hide abstract] 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.
International Conference on Autonomous Agents and Multiagent Systems (AAMAS); 05/2015
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
Annals of Mathematics and Artificial Intelligence 11/2014; 72(3-4):297-329. DOI:10.1007/s10472-014-9435-5 · 0.69 Impact Factor
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
Autonomous Agents and Multi-Agent Systems 11/2013; 28(6). DOI:10.1007/s10458-013-9244-y · 1.25 Impact Factor
[Show abstract][Hide abstract] 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.We analyze three variants of the problem, differing in their objective: minimizing the total expected cost, maximizing the success probability given an initial budget, and minimizing the budget necessary to obtain a given success probability. For each variant, we first introduce and analyze the problem with a single agent, either providing a polynomial solution to the problem or proving it is NP-complete. We also introduce a fully polynomial time approximation scheme algorithm for the minimum budget variant. In the multi-agent case, we analyze two models for managing resources, shared and private budget models. We present polynomial algorithms that work for any fixed number of agents, in the shared or private budget model. For non-communicating agents in the private budget model, we present a polynomial algorithm that is suitable for any number of agents. We also analyze the difference between homogeneous and heterogeneous agents, both with respect to their allotted resources and with respect to their capabilities. Finally, we define our problem in an environment with self-interested agents. We show how to find a Nash equilibrium in polynomial time, and prove that the bound on the performance of our algorithms, with respect to the social welfare, is tight.
[Show abstract][Hide abstract] 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.
Proceedings of the The 2012 IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technology - Volume 02; 12/2012
[Show abstract][Hide abstract] 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.
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 3; 06/2012
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
ACM Transactions on Algorithms 01/2012; DOI:10.1145/2151171.2151172 · 0.90 Impact Factor
[Show abstract][Hide abstract] 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.
Lecture Notes in Business Information Processing 01/2012; 118. DOI:10.1007/978-3-642-34200-4_6
[Show abstract][Hide abstract] 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.
[Show abstract][Hide abstract] 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.
Algorithmic Game Theory, 4th International Symposium, SAGT 2011, Amalfi, Italy, October 17-19, 2011. Proceedings; 01/2011
[Show abstract][Hide abstract] ABSTRACT: We consider the issue of fair division of goods, using the cake cutting abstraction, and aim to bound the possible degradation
in social welfare due to the fairness requirements. Previous work has considered this problem for the setting where the division
may allocate each player any number of unconnected pieces. Here, we consider the setting where each player must receive a
single connected piece. For this setting, we provide tight bounds on the maximum possible degradation to both utilitarian
and egalitarian welfare due to three fairness criteria — proportionality, envy-freeness and equitability.
Internet and Network Economics - 6th International Workshop, WINE 2010, Stanford, CA, USA, December 13-17, 2010. Proceedings; 01/2010
[Show abstract][Hide abstract] ABSTRACT: Coalitions and cooperation are key topics in multi-agent systems (mas). They enable agents to achieve goals that they may not have been able to achieve independently. A range of previous studies have found that many problems in coalitional games tend to be computationally intractable - that is, the computational complexity grows rapidly as a function of the number of participating agents. However, these hardness results generally require that each agent is of a different type. Here, we observe that in many mas settings, while the number of agents may grow, the number of different types of agents remains small. We formally define the notion of agent types in cooperative games. We then re-examine the computational complexity of the different coalition formation problems when assuming that the number of agent types is fixed. We show that most of the previously hard problems become polynomial when the number of agent types is fixed. We consider multiple different game formulations and representations (characteristic function with subadditive utilities, crg, and graphical representations) and several different computational problems (including stability, core-emptiness, and Shapley value).
9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), Toronto, Canada, May 10-14, 2010, Volume 1-3; 01/2010