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30
Cooperative Boolean Games
, 2008
"... We present and formally investigate Cooperative Boolean Games, a new, natural family of coalitional games that are both compact and expressive. In such a game, an agent’s primary aim is to achieve its individual goal, which is represented as a propositional logic formula over some set of Boolean var ..."
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Cited by 27 (15 self)
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We present and formally investigate Cooperative Boolean Games, a new, natural family of coalitional games that are both compact and expressive. In such a game, an agent’s primary aim is to achieve its individual goal, which is represented as a propositional logic formula over some set of Boolean variables. Each agent is assumed to exercise unique control over some subset of the overall set of Boolean variables, and the set of valuations for these variables corresponds to the set of actions the agent can take. However, the actions available to an agent are assumed to have some cost, and an agent’s secondary aim is to minimise its costs. Typically, an agent must cooperate with others because it does not have sufficient control to ensure its goal is satisfied. However, the desire to minimise costs leads to preferences over possible coalitions, and hence to strategic behaviour. Following an introduction to the formal framework of Cooperative Boolean Games, we investigate solution concepts of the core and stable sets for them. In each case, we characterise the complexity of the associated solution concept, and discuss the surrounding issues. Finally, we present a bargaining protocol for cooperation in Boolean games, and characterise the strategies in equilibrium for this protocol.
On the computational complexity of coalitional resource games
 Artificial Intelligence
"... www.elsevier.com/locate/artint We study Coalitional Resource Games (CRGs), a variation of Qualitative Coalitional Games (QCGs) in which each agent is endowed with a set of resources, and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with th ..."
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Cited by 26 (6 self)
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www.elsevier.com/locate/artint We study Coalitional Resource Games (CRGs), a variation of Qualitative Coalitional Games (QCGs) in which each agent is endowed with a set of resources, and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with the necessary resources. We investigate and classify the computational complexity of a number of natural decision problems for CRGs, over and above those previously investigated for QCGs in general. For example, we show that the complexity of determining whether conflict is inevitable between two coalitions with respect to some stated resource bound (i.e., a limit value for every resource) is coNPcomplete. We then investigate the relationship between CRGs and QCGs, and in particular the extent to which it is possible to translate between the two models. We first characterise the complexity of determining equivalence between CRGs and QCGs. We then show that it is always possible to translate any given CRG into a succinct equivalent QCG, and that it is not always possible to translate a QCG into an equivalent CRG; we establish some necessary and some sufficient conditions for a translation from QCGs to CRGs to be possible, and show that even where an equivalent CRG exists, it may have size exponential in the number of goals and agents of its source QCG.
Extremal Behaviour in Multiagent Contract Negotiation
 Journal of Artificial Intelligence Research
, 2004
"... We examine properties of a model of resource allocation in which several agents exchange resources in order to optimise their individual holdings. The schemes discussed relate to wellknown negotiation protocols proposed in earlier work and we consider a number of alternative notions of "rational ..."
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Cited by 24 (7 self)
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We examine properties of a model of resource allocation in which several agents exchange resources in order to optimise their individual holdings. The schemes discussed relate to wellknown negotiation protocols proposed in earlier work and we consider a number of alternative notions of "rationality" covering both quantitative measures, e.g. cooperative and individual rationality and more qualitative forms, e.g. PigouDalton transfers. While it is known that imposing particular rationality and structural restrictions on the form of exchanges may render these unable to realise every reallocation of the resource set, in this paper we address the issue of the number of restricted rational exchanges that may be required to implement a particular reallocation when it is possible to do so. We construct examples showing that this number may be exponential (in the number of resources m), even when all of the agent utility functions are monotonic. We further show that k agents may achieve in a single exchange a reallocation requiring exponentially many rational exchanges if at most k 1 agents can participate, this same reallocation being unrealisable by any sequences of rational exchanges in which at most k 2 agents are involved.
Coalitional Skill Games
"... We consider Coalitional Skill Games (CSGs), a simple model of cooperation among agents. This is a restricted form of coalitional games, where each agent has a set of skills that are required to complete various tasks. Each task requires a set of skills in order to be completed, and a coalition can a ..."
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Cited by 19 (8 self)
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We consider Coalitional Skill Games (CSGs), a simple model of cooperation among agents. This is a restricted form of coalitional games, where each agent has a set of skills that are required to complete various tasks. Each task requires a set of skills in order to be completed, and a coalition can accomplish the task only if the coalition’s agents cover the set of required skills for the task. The gain for a coalition depends only on the subset of tasks it can complete. We consider the computational complexity of several problems in CSGs, for example, testing if an agent is a dummy or veto agent, computing the core of the game or testing whether the core is empty, and finding the Shapley value or Banzhaf power index of agents.
Coalition Structure Generation Utilizing Compact Characteristic Function Representations (Extended Abstract)
"... Forming e ective coalitions is a major research challenge in AI and multiagent systems. Coalition structure generation (CSG), which involves partitioning a set of agents into coalitions so that social surplus is maximized, is a central research topic due to its computational complexity. In this pap ..."
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Cited by 17 (3 self)
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Forming e ective coalitions is a major research challenge in AI and multiagent systems. Coalition structure generation (CSG), which involves partitioning a set of agents into coalitions so that social surplus is maximized, is a central research topic due to its computational complexity. In this paper, we present new methods for CSG utilizing recently developed compact representation schemes for characteristic functions. We characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of synergy coalition groups than by the number of agents. Furthermore, we develop mixed integer programming formulations and show that an otheshelf optimization package can solve these problems quite e ciently.
Quantified coalition logic
, 2008
"... We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in gamelike multiagent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achi ..."
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Cited by 14 (9 self)
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We add a limited but useful form of quantification to Coalition Logic, a popular formalism for reasoning about cooperation in gamelike multiagent systems. The basic constructs of Quantified Coalition Logic (QCL) allow us to express such properties as “every coalition satisfying property P can achieve ϕ ” and “there exists a coalition C satisfying property P such that C can achieve ϕ”. We give an axiomatisation of QCL, and show that while it is no more expressive than Coalition Logic, it is nevertheless exponentially more succinct. The complexity of QCL model checking for symbolic and explicit state representations is shown to be no worse than that of Coalition Logic, and satisfiability for QCL is shown to be no worse than satisfiability for Coalition Logic. We illustrate the formalism by showing how to succinctly specify such social choice mechanisms as majority voting, which in Coalition Logic require specifications that are exponentially long in the number of agents.
Logic for Automated Mechanism Design  A Progress Report
 IN TWENTYSECOND CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI07), 2007. INSTITUTE OF LOGIC, LANGUAGE AND COMPUTATION, UNIVERSITY OF AMSTERDAM, PLANGTAGE MUIDERGRACHT 24, 1018 TV, AMSTERDAM EMAIL ADDRESS: EPACUIT@SCIENCE.UVA.NL
, 2007
"... Over the past half decade, we have been exploring the use of logic in the specification and analysis of computational economic mechanisms. We believe that this approach has the potential to bring the same benefits to the design and analysis of computational economic mechanisms that the use of tempor ..."
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Cited by 10 (1 self)
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Over the past half decade, we have been exploring the use of logic in the specification and analysis of computational economic mechanisms. We believe that this approach has the potential to bring the same benefits to the design and analysis of computational economic mechanisms that the use of temporal logics and model checking have brought to the specification and analysis of reactive systems. In this paper, we give a survey of our work. We first discuss the use of cooperation logics such as Alternatingtime Temporal Logic (ATL) for the specification and verification of mechanisms such as social choice procedures. We motivate the approach, and then discuss the work we have done on extensions to ATL to support incomplete information, preferences, and quantification over coalitions. We then discuss is the use of ATLlike cooperation logics in the development of social laws.
Strengthening admissible coalitions
 in: Procs. of the 17th European Conference on Artificial Intelligence (ECAI’06
, 2006
"... Abstract. We develop a criterion for coalition formation among goaldirected agents, the indecomposable doutdes property. The indecomposable doutdes property refines the doutdes property (literally give to get) by considering the fact that agents prefer to form coalitions whose components cann ..."
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Cited by 10 (6 self)
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Abstract. We develop a criterion for coalition formation among goaldirected agents, the indecomposable doutdes property. The indecomposable doutdes property refines the doutdes property (literally give to get) by considering the fact that agents prefer to form coalitions whose components cannot be formed independently. A formal description of this property is provided as well as an analysis of algorithms and their complexity. 1
On agent types in coalition formation problems
 In Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS
, 2010
"... 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 c ..."
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Cited by 8 (0 self)
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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 reexamine 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, coreemptiness, and Shapley value).