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36
The organization of thinking: What functional brain imaging reveals about the neuroarchitecture of complex cognition
, 2007
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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 36 (16 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.
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 35 (10 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 22 (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.
Efficient Computation of the Shapley Value for GameTheoretic Network Centrality
"... The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of realworld applications (including social and organisational networks, biolo ..."
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Cited by 13 (3 self)
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The Shapley value—probably the most important normative payoff division scheme in coalitional games—has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of realworld applications (including social and organisational networks, biological networks and communication networks), its computational properties have not been widely studied. To date, the only practicable approach to compute Shapley valuebased centrality has been via Monte Carlo simulations which are computationally expensive and not guaranteed to give an exact answer. Against this background, this paper presents the first study of the computational aspects of the Shapley value for network centralities. Specifically, we develop exact analytical formulae for Shapley valuebased centrality in both weighted and unweighted networks and develop efficient (polynomial time) and exact algorithms based on them. We empirically evaluate these algorithms on two reallife examples (an infrastructure network representing the topology of the Western States Power Grid and a collaboration network from the field of astrophysics) and demonstrate that they deliver significant speedups over the Monte Carlo approach. For
Logic for automated mechanism design  a progress report
 In Proceedings of AAAI07
, 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 temp ..."
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Cited by 12 (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.
A LogicBased Representation for Coalitional Games with Externalities
, 2010
"... We consider the issue of representing coalitional games in multiagent systems that exhibit externalities from coalition formation, i.e., systems in which the gain from forming a coalition may be affected by the formation of other coexisting coalitions. Although externalities play a key role in many ..."
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Cited by 12 (7 self)
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We consider the issue of representing coalitional games in multiagent systems that exhibit externalities from coalition formation, i.e., systems in which the gain from forming a coalition may be affected by the formation of other coexisting coalitions. Although externalities play a key role in many reallife situations, very little attention has been given to this issue in the multiagent system literature, especially with regard to the computational aspects involved. To this end, we propose a new representation which, in the spirit of Ieong and Shoham [9], is based on Boolean expressions. The idea behind our representation is to construct much richer expressions that allow for capturing externalities induced upon coalitions. We show that the new representation is fully expressive, at least as concise as the conventional partition function game representation and, for many games, exponentially more concise. We evaluate the
Efficient Computation of the Shapley Value for Centrality in Networks
"... Abstract. The Shapley Value is arguably the most important normative solution concept in coalitional games. One of its applications is in the domain of networks, where the Shapley Value is used to measure the relative importance of individual nodes. This measure, which is called node centrality, is ..."
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Cited by 9 (4 self)
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Abstract. The Shapley Value is arguably the most important normative solution concept in coalitional games. One of its applications is in the domain of networks, where the Shapley Value is used to measure the relative importance of individual nodes. This measure, which is called node centrality, is of paramount significance in many realworld application domains including social and organisational networks, biological networks, communication networks and the internet. Whereas computational aspects of the Shapley Value have been analyzed in the context of conventional coalitional games, this paper presents the first such study of the Shapley Value for network centrality. Our results demonstrate that this particular application of the Shapley Value presents unique opportunities for efficiency gains. In particular, we develop exact analytical formulas for computing Shapley Value based centralities in both weighted and unweighted networks. These formulas not only provide an efficient (polynomial time) and errorfree way of computing node centralities, but their surprisingly simple closed form expressions also offer intuition into why certain nodes are relatively more important to a network. 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).