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Coalition Structure Generation with Worst Case Guarantees
, 1999
"... Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition ..."
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Cited by 209 (10 self)
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Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NPcomplete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum? We show that none of the previous coalition structure generation algorithms can establish any bound because they search fewer nodes than a threshold that we show necessary for establishing a bound. We present an algorithm that establishes a tight bound within this minimal amount of search, and show that any other algorithm would have to search strictly more. The fraction of nodes needed to be searched approaches zero as the number of agents grows. If additional time remains, our anytime algorithm searches further, and establishes a progressively lower tight bound. Surprisingly, just searching one more node drops the bound in half. As desired, our algorithm lowers the bound rapidly early on, and exhibits diminishing returns to computation. It also significantly outperforms its obvious contenders. Finally, we show how to distribute the desired
A Survey of MultiAgent Organizational Paradigms
 The Knowledge Engineering Review
, 2005
"... Many researchers have demonstrated that the organizational design employed by a system can have a significant, quantitative effect on its performance characteristics. A range of organizational strategies have emerged from this line of research, each with different strengths and weaknesses. In this a ..."
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Cited by 55 (1 self)
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Many researchers have demonstrated that the organizational design employed by a system can have a significant, quantitative effect on its performance characteristics. A range of organizational strategies have emerged from this line of research, each with different strengths and weaknesses. In this article we present a survey of the major organizational paradigms used in multiagent systems. These include hierarchies, holarchies, coalitions, teams, congregations, societies, federations, and matrix organizations. We will provide a description of each, discuss their costs and benefits, and provide examples of how they may be instantiated and maintained. 1
Complexity of Determining Nonemptiness of the Core
, 2002
"... Coalition formation is a key problem in automated negotiation among selfinterested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can do things more efficiently. However, ..."
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Cited by 42 (5 self)
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Coalition formation is a key problem in automated negotiation among selfinterested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can do things more efficiently. However,
Agents in electronic commerce: component technologies for automated negotiation and coalition formation
 Autonomous Agents and MultiAgent Systems
"... Abstract. Automated negotiation and coalition formation among selfinterested agents are playing an increasingly important role in electronic commerce. Such agents cannot be coordinated by externally imposing their strategies. Instead the interaction protocols have to be designed so that each agent ..."
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Cited by 39 (1 self)
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Abstract. Automated negotiation and coalition formation among selfinterested agents are playing an increasingly important role in electronic commerce. Such agents cannot be coordinated by externally imposing their strategies. Instead the interaction protocols have to be designed so that each agent is motivated to follow the strategy that the protocol designer wants it to follow. This paper reviews six component technologies that we have developed for making such interactions less manipulable and more efficient in terms of the computational processes and the outcomes: 1. OCSMcontracts in marginal cost based contracting, 2. leveled commitment contracts, 3. anytime coalition structure generation with worst case guarantees, 4. trading off computation cost against optimization quality within each coalition, 5. distributing search among insincere agents, and 6. unenforced contract execution. Each of these technologies represents a different way of battling selfinterest and combinatorial complexity simultaneously. This is a key battle when multiagent systems move into largescale open settings.
Complexity of Constructing Solutions in the Core Based on Synergies among Coalitions
 ARTIFICIAL INTELLIGENCE
, 2006
"... Coalition formation is a key problem in automated negotiation among selfinterested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can accomplish them more efficiently. Motivating the agents to abide by a solut ..."
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Cited by 34 (1 self)
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Coalition formation is a key problem in automated negotiation among selfinterested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can accomplish them more efficiently. Motivating the agents to abide by a solution requires careful analysis: only some of the solutions are stable in the sense that no group of agents is motivated to break off and form a new coalition. This constraint has been studied extensively in cooperative game theory: the set of solutions that satisfy it is known as the core. The computational questions around the core have received less attention. When it comes to coalition formation among software agents (that represent realworld parties), these questions become increasingly explicit. In this
An anytime algorithm for optimal coalition structure generation
 Journal of Artificial Intelligence Research (JAIR
"... Coalition formation is a fundamental type of interaction that involves the creation of coherent groupings of distinct, autonomous, agents in order to efficiently achieve their individual or collective goals. Forming effective coalitions is a major research challenge in the field of multiagent syste ..."
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Cited by 31 (13 self)
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Coalition formation is a fundamental type of interaction that involves the creation of coherent groupings of distinct, autonomous, agents in order to efficiently achieve their individual or collective goals. Forming effective coalitions is a major research challenge in the field of multiagent systems. Central to this endeavour is the problem of determining which of the many possible coalitions to form in order to achieve some goal. This usually requires calculating a value for every possible coalition, known as the coalition value, which indicates how beneficial that coalition would be if it was formed. Once these values are calculated, the agents usually need to find a combination of coalitions, in which every agent belongs to exactly one coalition, and by which the overall outcome of the system is maximized. However, this coalition structure generation problem is extremely challenging due to the number of possible solutions that need to be examined, which grows exponentially with the number of agents involved. To date, therefore, many algorithms have been proposed to solve this problem using different techniques — ranging from dynamic programming, to integer programming, to stochastic search — all of which suffer from major limitations relating to execution time, solution quality, and memory requirements.
Longterm coalitions for the electronic marketplace
 Proceedings of the ECommerce Applications Workshop, Canadian AI Conference
, 2001
"... This paper presents a new coalition formation mechanism for the electronic marketplace that extends the existing transactionoriented coalitions to longterm ones based on nurturing customervendor relationships. Because trust is an important factor in any form of commerce and it has been an elabora ..."
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Cited by 23 (3 self)
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This paper presents a new coalition formation mechanism for the electronic marketplace that extends the existing transactionoriented coalitions to longterm ones based on nurturing customervendor relationships. Because trust is an important factor in any form of commerce and it has been an elaborated issue in Electronic Commerce applications in the last few years, we use trust based relationships between agents to model other agents and to help an agent when faced with the decision making problem of joining or leaving a coalition. Microscopic (agent level) description of the proposed coalition formation mechanism based on trust relationships between agents is provided.
Anytime optimal coalition structure generation
 In Proceedings of the 22nd National Conference on Artificial Intelligence
, 2007
"... Abstract. Forming effective coalitions is a major research challenge in the field of multiagent systems. Central to this endeavour is the problem of determining the best groups of agents to select to achieve some goal. To this end, in this paper, we present a novel, optimal anytime algorithm for th ..."
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Cited by 20 (6 self)
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Abstract. Forming effective coalitions is a major research challenge in the field of multiagent systems. Central to this endeavour is the problem of determining the best groups of agents to select to achieve some goal. To this end, in this paper, we present a novel, optimal anytime algorithm for this coalition structure generation problem that is significantly faster than previous algorithms designed for this purpose. Specifically, our algorithm can generate solutions by partitioning the space of all potential coalitions into subspaces that contain coalition structures that are similar, according to some criterion, such that these subspaces can be pruned by identifying their bounds. Using this representation, the algorithm then searches through only valid and unique coalition structures and selects the best among them using a branchandbound technique. We empirically show that we are able to find solutions that are optimal in 0.082 % of the time taken by the state of the art dynamic programming algorithm (for 27 agents) using much less memory (O(2 A  ) instead of O(3 A  ) for the set of agents A). Moreover, our algorithm is the first to be able to solve the coalition structure generation problem for numbers of agents bigger than 27 in reasonable time (less than 90 minutes for 27 agents as opposed to around 2 months for the best previous solution). 1
Nearoptimal anytime coalition structure generation
 In Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI07
, 2007
"... Forming effective coalitions is a major research challenge in the field of multiagent systems. Central to this endeavour is the problem of determining the best set of agents that should participate in a given team. To this end, in this paper, we present a novel, anytime algorithm for coalition stru ..."
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Cited by 16 (4 self)
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Forming effective coalitions is a major research challenge in the field of multiagent systems. Central to this endeavour is the problem of determining the best set of agents that should participate in a given team. To this end, in this paper, we present a novel, anytime algorithm for coalition structure generation that is faster than previous anytime algorithms designed for this purpose. Our algorithm can generate solutions that either have a tight bound from the optimal or are optimal (depending on the objective) and works by partitioning the space in terms of a small set of elements that represent structures which contain coalitions of particular sizes. It then performs an online heuristic search that prunes the space and only considers valid and nonredundant coalition structures. We empirically show that we are able to find solutions that are, in the worst case, 99 % efficient in 0.0043% of the time to find the optimal value by the state of the art dynamic programming (DP) algorithm (for 20 agents), using 33 % less memory. 1
Coalition structure generation: dynamic programming meets anytime optimisation
 In Proceedings of the Twenty Third Conference on Artificial Intelligence
, 2008
"... Coalition structure generation involves partitioning a set of agents into exhaustive and disjoint coalitions so as to maximize the social welfare. What makes this such a challenging problem is that the number of possible solutions grows exponentially as the number of agents increases. To date, two m ..."
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Cited by 12 (7 self)
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Coalition structure generation involves partitioning a set of agents into exhaustive and disjoint coalitions so as to maximize the social welfare. What makes this such a challenging problem is that the number of possible solutions grows exponentially as the number of agents increases. To date, two main approaches have been developed to solve this problem, each with its own strengths and weaknesses. The state of the art in the first approach is the Improved Dynamic Programming (IDP) algorithm, due to Rahwan and Jennings, that is guaranteed to find an optimal solution in O(3 n), but which cannot generate a solution until it has completed its entire execution. The state of the art in the second approach is an anytime algorithm called IP, due to Rahwan et al., that provides worstcase guarantees on the quality of the best solution found so far, but which is O(n n). In this paper, we develop a novel algorithm that combines both IDP and IP, resulting in a hybrid performance that exploits the strength of both algorithms and, at the same, avoids their main weaknesses. Our approach is also significantly faster (e.g. given 25 agents, it takes only 28 % of the time required by IP, and 0.3 % of the time required by IDP).