Task execution in multi-agent environments may require cooperation among agents. Given a set of agents and a set of tasks which they have to satisfy, we consider situations where each task should be attached to a group of agents that will perform the task. Task allocation to groups of agents is necessary when tasks cannot be performed by a single agent. However it may also be beneficial when groups perform more efficiently with respect to the single agents' performance. In this paper we present several solutions to the problem of task allocation among autonomous agents, and suggest that the agents form coalitions in order to perform tasks or improve the efficiency of their performance. We present efficient distributed algorithms with low ratio bounds and with low computational complexities. These properties are proven theoretically and supported by simulations and an implementation in an agent system. Our methods are based on both the algorithmic aspects of combinatorics and approximat...

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 NP-complete. 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

This paper analyzes coalitions among self-interested agents that need to solve combinatorial optimization problems to operate e ciently in the world. By colluding (coordinating their actions by solving a joint optimization prob-lem) the agents can sometimes save costs compared to operating individually. A model of bounded rationality is adopted where computation resources are costly. It is not worthwhile solving the problems optimally: solution quality is decision-theoretically traded o against computation cost. A normative, application- and protocol-independent theory of coalitions among bounded-rational agents is devised. The optimal coalition structure and its stability are signi cantly a ected by the agents ' algorithms ' performance pro les and the cost of computation. This relationship is rst analyzed theoretically. Then a domain classi cation including rational and bounded-rational agents is in-troduced. Experimental results are presented in vehicle routing with real data from ve dispatch centers. This problem is NP-complete and the instances are so large that|with current technology|any agent's rationality is bounded by computational complexity. 1

Automated intelligent agents inhabiting a shared environmentmust coordinate their activities. Cooperation { not merely coordination { may improve the performance of the individual agents or the overall behavior of the system they form. Research in Distributed Arti cial Intelligence (DAI) addresses the problem of designing automated intelligent systems which interact e ectively. DAI is not the only eld to take on the challenge of understanding cooperation and coordination. There are a variety of other multi-entity environments in which the entities coordinate their activity and cooperate. Among them are groups of people, animals, particles, and computers. We argue that in order to address the challenge of building coordinated and collaborated intelligent agents, it is bene cial to combine AI techniques with methods and techniques from a range of multi-entity elds, such as game theory, operations research, physics and philosophy. To support this claim, we describe some of our projects, where we have successfully taken an interdisciplinary approach. We demonstrate the bene ts in applying multi-entity methodologies and show the adaptations, modi cations and extensions necessary for solving the DAI problems.

This paper analyzes coalition formation among self-interested agents that need to solve combinatorial optimization problems to operate efficiently in the world. By colluding (coordinating their actions by solving a joint optimization problem), the agents can sometimes save costs compared to operating individually. A model of bounded rationality is adopted, where computation resources are costly. It is not worth solving the problems optimally: solution quality is decision-theoretically traded off against computation cost. A normative theory of coalitions among bounded rational (BR) agents is devised. The optimal coalition structure and its stability are significantly affected by the agents ' algorithms ' performance profiles (PPs) and the cost of computation. This relationship is first analyzed theoretically. A domain classification including rational and BR agents is introduced. Experimental results are presented in the distributed vehicle routing domain using real data from 5 dispatch centers; the optimal coalition structure for BR agents differs significantly from the one for rational agents. These problems are NP-complete and the instances are so large that, with current technology, any agent's rationality is bounded by computational complexity. 1

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The coalition formation process, in which a number of independent, autonomous agents come together to act as a collective, is an important form of interaction in multiagent systems. When e#ective, such coalitions can improve the performance of the individual agents and/or of the system as a whole. However, one of the main problems that hinders the wide spread adoption of coalition formation technologies is the computational complexity of coalition structure generation. That is, once a group of agents has been identified, how can it be partitioned in order to maximise the social payoff? This problem has been shown to be NP-hard and even finding a sub-optimal solution requires searching an exponential number of solutions. Against this background, this paper reports on a novel anytime algorithm for coalition structure generation that produces solutions that are within a finite bound from the optimal. Our algorithm is benchmarked against Sandholm et al.'s algorithm [8] (the only other known algorithm for this task that can also establish a worst-case bound from the optimal) and is shown to be up to 10^379 times faster (for systems containing 1000 agents) when small bounds from the optimal are desirable.

Cooperating and sharing resources by creating coalitions of agents are an important way for autonomous agents to execute tasks and to maximize payoff. Such coalitions will form only if each member of a coalition gains more if it joins the coalition than it could gain otherwise. There are several ways of creating such coalitions and dividing the joint payoff among the members. In this paper we present algorithms for coalition formation and payoff distribution in non-super-additive environments. We focus on a low-complexity kernel-oriented coalition formation algorithm. The properties of this algorithm were examined via simulations. These have shown that the model increases the benefits of the agents within a reasonable time period, and more coalition formations provide more benefits to the agents. Key Words Distributed AI, Coalition Formation, Multi-Agent Systems. This material is based upon work supported in part by the NSF under grant No. IRI-9423967, ARPA/Rome Labs contract F30602...

Coalition formation methods allow agents to join together and are thus necessary in cases where tasks can only be performed cooperatively by groups. This is the case in the Request For Proposal (RFP) domain, where some requester business agent issues an RFP - a complex task comprised of sub-tasks - and several service provider agents need to join together to address this RFP. In such environments the value of the RFP may be common knowledge, however the costs that an agent incurs for performing a specific sub-task are unknown to other agents. Additionally, time for addressing RFPs is limited. These constraints make it hard to apply traditional coalition formation mechanisms, since those assume complete information, and time constraints are of lesser significance there. To address this problem, we have developed a protocol that enables agents to negotiate and form coalitions, and provide them with simple heuristics for choosing coalition partners. The protocol and the heuristics allow the agents to form coalitions in the face of time constraints and incomplete information. The overall payoff of agents using our heuristics is very close to an experimentally measured optimal value, as our extensive experimental evaluation shows. Categories and Subject Descriptors I.2.11 [Distributed Artificial Intelligence]: Multi-agent Systems, Coherence and Coordination, Intelligent Agents.

This article proposes a simulation-based DCF scheme designed to let rational agents form coalitions in dynamic environments