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Computing Desirable Partitions in Additively Separable Hedonic Games
, 2011
"... An important aspect in systems of multiple autonomous agents is the exploitation of synergies via coalition formation. Additively separable hedonic games are a fundamental class of coalition formation games in which each player has a value for any other player and the value of a coalition to a parti ..."
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Cited by 11 (4 self)
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An important aspect in systems of multiple autonomous agents is the exploitation of synergies via coalition formation. Additively separable hedonic games are a fundamental class of coalition formation games in which each player has a value for any other player and the value of a coalition to a particular player is simply the sum of the values he assigns to the members of his coalition. In this paper, we consider a number of solution concepts from cooperative game theory, welfare theory, and social choice theory as criteria for desirable partitions in hedonic games. We then conduct a detailed computational analysis of computing, checking the existence of, and verifying stable, fair, optimal, and popular partitions for additively separable hedonic games.
Group activity selection problem
 In Proceedings of WINE12
, 2012
"... We consider a setting where we have to organize one or several group activities for a group of agents. Each agent will participate in at most one activity; her preference over activities generally depends on the number of participants in the activity. The goal is to assign agents to activities in a ..."
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Cited by 10 (3 self)
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We consider a setting where we have to organize one or several group activities for a group of agents. Each agent will participate in at most one activity; her preference over activities generally depends on the number of participants in the activity. The goal is to assign agents to activities in a desirable way. We give a general model, which is a natural generalization of anonymous hedonic games (and can also be expressed, in a less natural way, as a hedonic game). Two wellknown solution concepts in hedonic games, namely individual rationality and Nash stability, are particularly meaningful for our model. We study, from the computational point of view, some existence and optimization problems related to these two solution concepts, in the general case as well as for natural restrictions on the agents ’ preferences. 1
Fractional Hedonic Games
"... An important issue in multiagent systems is the exploitation of synergies via coalition formation. We initiate the formal study of fractional hedonic games. In fractional hedonic games, the utility of a player in a coalition structure is the average value he ascribes to the members of his coalition ..."
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Cited by 6 (2 self)
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An important issue in multiagent systems is the exploitation of synergies via coalition formation. We initiate the formal study of fractional hedonic games. In fractional hedonic games, the utility of a player in a coalition structure is the average value he ascribes to the members of his coalition. Among other settings, this covers situations in which there are several types of agents and each agent desires to be in a coalition in which the fraction of agents of his own type is minimal. Fractional hedonic games not only constitute a natural class of succinctly representable coalition formation games, but also provide an interesting framework for network clustering. We propose a number of conditions under which the core of fractional hedonic games is nonempty and provide algorithms for computing a core stable outcome.
Finegrained Interoperability through Mirrors and Contracts
, 2005
"... As a value flows across the boundary between interoperating languages, it must be checked and converted to fit the types and representations of the target language. For simple forms of data, the checks and coercions can be immediate; for higher order data, such as functions and objects, some must be ..."
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Cited by 3 (0 self)
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As a value flows across the boundary between interoperating languages, it must be checked and converted to fit the types and representations of the target language. For simple forms of data, the checks and coercions can be immediate; for higher order data, such as functions and objects, some must be delayed until the value is used in a particular way. Typically, these coercions and checks are implemented by an adhoc mixture of wrappers, reflection, and dynamic predicates. We observe that 1) the wrapper and reflection operations fit the profile of mirrors, 2) the checks correspond to contracts, and 3) the timing and shape of mirror operations coincide with the timing and shape of contract operations. Based on these insights, we present a new model of interoperability that builds on the ideas of mirrors and contracts, and we describe an interoperable implementation of Java and Scheme that is guided by the model.
Fractional Hedonic Games: Individual and Group Stability
"... Coalition formation provides a versatile framework for analyzing cooperative behavior in multiagent systems. In particular, hedonic coalition formation has gained considerable attention in the literature. An interesting class of hedonic games recently introduced by Aziz et al. [3] are fractional ..."
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Coalition formation provides a versatile framework for analyzing cooperative behavior in multiagent systems. In particular, hedonic coalition formation has gained considerable attention in the literature. An interesting class of hedonic games recently introduced by Aziz et al. [3] are fractional hedonic games. In these games, the utility an agent assigns to a coalition is his average valuation for the members of his coalition. Three common notions of stability in hedonic games are core stability, Nash stability, and individual stability. For each of these notions we show that stable partitions may fail to exist in fractional hedonic games. For core stable partitions this holds even when all players only have symmetric zero/one valuations (“mutual friendship”). We then leverage these counterexamples to show that deciding the existence of stable partitions (and therefore also computing stable partitions) is NPhard for all considered stability notions. Moreover, we show that checking whether the valuation functions of a fractional hedonic game induce strict preferences over coalitions is coNPcomplete. Categories and Subject Descriptors [Theory of computation]: Algorithmic game theory; [Theory of computation]: Solution concepts in game theory; [Theory of computation]: Computational complexity and cryptography; [Computing methodologies]: Multiagent systems; [Mathematics of computing]: Graph theory
Simple Causes of Complexity in Hedonic Games
"... Hedonic games provide a natural model of coalition formation among selfinterested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on expressivity of hedonic games that are sufficient for the problem ..."
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Hedonic games provide a natural model of coalition formation among selfinterested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on expressivity of hedonic games that are sufficient for the problem of checking whether a given game admits a stable outcome to be computationally hard. Somewhat surprisingly, these conditions are very mild and intuitive. Our results apply to a wide range of stability concepts (core stability, individual stability, Nash stability, etc.) and to many known formalisms for hedonic games (additively separable games, games withWpreferences, fractional hedonic games, etc.), and unify and extend known results for these formalisms. They also have broader applicability: for several classes of hedonic games whose computational complexity has not been explored in prior work, we show that our framework immediately implies a number of hardness results for them. 1
Roles and Teams Hedonic Game
"... Abstract. We introduce a new variant of hedonic coalition formation games in which agents have two levels of preference on their own coalitions: preference on the set of “roles ” that makes up the coalition, and preference on their own role within the coalition. We define several stability notions ..."
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Abstract. We introduce a new variant of hedonic coalition formation games in which agents have two levels of preference on their own coalitions: preference on the set of “roles ” that makes up the coalition, and preference on their own role within the coalition. We define several stability notions and optimization problems for this model. We prove the hardness of the decision problems related to our optimization criteria and show easiness of finding individually stable partitions. We introduce a heuristic optimizer for coalition formation in this setting. We evaluate results of the heuristic optimizer and the results of local search for individually stable partitions with respect to bruteforce MaxSum and MaxMin solvers.
Finding the Pareto Curve in Bimatrix Games is Easy
"... Pareto efficiency is a widely used property in solution concepts for cooperative and non–cooperative game–theoretic settings and, more generally, in multi–objective problems. However, finding or even approximating (when the objective functions are not convex) the Pareto curve is hard. Most of the l ..."
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Pareto efficiency is a widely used property in solution concepts for cooperative and non–cooperative game–theoretic settings and, more generally, in multi–objective problems. However, finding or even approximating (when the objective functions are not convex) the Pareto curve is hard. Most of the literature focuses on computing concise representations to approximate the Pareto curve or on exploiting evolutionary approaches to generate approximately Pareto efficient samples of the curve. In this paper, we show that the Pareto curve of a bimatrix game can be found exactly in polynomial time and that it is composed of a polynomial number of pieces. Furthermore, each piece is a quadratic function. We use this result to provide algorithms for gametheoretic solution concepts that incorporate Pareto efficiency.
Universal Pareto Dominance and Welfare for Plausible Utility Functions
, 2014
"... We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents ’ preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto un ..."
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We study Pareto efficiency in a setting that involves two kinds of uncertainty: Uncertainty over the possible outcomes is modeled using lotteries whereas uncertainty over the agents ’ preferences over lotteries is modeled using sets of plausible utility functions. A lottery is universally Pareto undominated if there is no other lottery that Pareto dominates it for all plausible utility functions. We show that, under fairly general conditions, a lottery is universally Pareto undominated iff it is Pareto efficient for some vector of plausible utility functions, which in turn implies affine welfare maximization for this vector. In contrast to previous work on linear utility functions, we use the significantly more general framework of skewsymmetric bilinear (SSB) utility functions as introduced by Fishburn (1982). Our main theorem generalizes a theorem by Carroll (2010) and implies the ordinal efficiency welfare theorem. We discuss three natural classes of plausible utility functions, which lead to three notions of ordinal efficiency, including stochastic dominance, and conclude with a detailed investigation of the geometric and computational properties of these notions. 1
Existence of Stability in Hedonic Coalition Formation
"... In this paper, we examine hedonic coalition formation games in which each player’s preferences over partitions of players depend only on the members of his coalition. We present three main results in which restrictions on the preferences of the players guarantee the existence of stable partitions fo ..."
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In this paper, we examine hedonic coalition formation games in which each player’s preferences over partitions of players depend only on the members of his coalition. We present three main results in which restrictions on the preferences of the players guarantee the existence of stable partitions for various notions of stability. The preference restrictions pertain to top responsiveness and bottom responsiveness which model optimistic and pessimistic behavior of players respectively. The existence results apply to natural subclasses of additively separable hedonic games and hedonic games with Bpreferences. It is also shown that our existence results cannot be strengthened to the case of stronger known stability concepts.