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

Introduction Automated negotiation systems with self-interested agents are becoming increasingly important. One reason for this is the technology push of a growing standardized communication infrastructure---Internet, WWW, NII, EDI, KQML, FIPA, Concordia, Voyager, Odyssey, Telescript, Java, etc---over which separately designed agents belonging to different organizations can interact in an open environment in realtime and safely carry out transactions. The second reason is strong application pull for computer support for negotiation at the operative decision making level. For example, we are witnessing the advent of small transaction electronic commerce on the Internet for purchasing goods, information, and communication bandwidth [29]. There is also an industrial trend toward virtual enterprises: dynamic alliances of small, agile enterprises which together can take advantage of economies of scale when available (e.g., respond to mor

Coalition formation is a key problem in automated negotiation among self-interested 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,

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 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 real-world parties), these questions become increasingly explicit. In this

Abstract. Coalition formation is a key topic in multiagent systems. One would 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 for exhaustive search for the optimal one. We present experimental results for three anytime algorithms that search the space of coalition structures. We show that, in the average case, all three algorithms do much better than the recently established theoretical worst case results in Sandholm et al. (1999a). We also show that no one algorithm is dominant. Each algorithm’s performance is in¯uenced by the particular instance distribution, with each algorithm outperforming the others for diŒerent instances. We present a possible explanation for the behaviour of the algorithms and support our hypothesis with data collected from a controlled experimental run. K eywords: coalition structure, algorithm, multiagent systems 1.

In an electronic marketplace coalition formation allows buyers to enjoy a price discount for each item while combinatorial auction enables buyers to place bids for a bundle of items that are complementary. Coalition formation and combinatorial auction both help to improve the efficiency of a market and have received much attention from economists and computer scientists. But neither in laboratories nor in practice has there been literature on the situations where both coalition formation and combinatorial auctions exist. In this paper we consider an e-market where each buyer places a bid on a combination of items with a reservation cost, and sellers offer price discounts for each item based on volumes. We call coalition formation under this condition a Combinatorial Coalition Formation (CCF) problem since coalition formation is motivated by price discounts on single items while multiple items are complementary for buyers. By artificially dividing the reservation cost of each buyer appropriately among the items we can construct optimal coalitions with respect to each item. We then try to make these coalitions satisfy the complementarity of the items, and thus induce the optimal solution. Based on this idea we present polynomial-time algorithms to find a semi-optimal solution of CCF and a payoff division scheme that is in the core of the coalition when linear price functions are applied, and in the pseudo-core when general price functions are applied. Simulation results show that the algorithms obtain solutions in a satisfactory ratio to the optimal value.

In this paper we present a model for coalition formation and payoff distribution in general environments. We focus on a reduced complexity kernel-oriented coalition formation model, and provide a detailed algorithm for the activity of the single rational agent. The model is partitioned into a social level and a strategic level, to distinguish between regulations that must be agreed upon and are forced by agent-designers, and strategies by which each agent acts at will. In addition, we present an implementation of the model and simulation results. From these we conclude that implementing the model for coalition formation among agents increases the benefits of the agents with reasonable time consumption. It also shows that more coalition formations yield more benefits to the agents. Introduction An important method for cooperation in multi-agent environments is coalition formation. Membership in a coalition may increase the agent's ability to satisfy its goals and maximize its own pers...

A problem that has recently attracted the attention of the research community is the autonomous formation of robot teams to perform complex multirobot tasks. The corresponding problem for software agents is also known in the multi-agent community as the coalition formation problem. Numerous algorithms for software agent coalition formation have been provided that allow for efficient cooperation in both competitive and cooperative environments. However, despite the plethora of relevant literature on the software agent coalition formation problem, and the existence of similar problems in theoretical computer science, the multirobot coalition formation problem has not been sufficiently grounded for different tasks and task environments. In this paper, comparisons are drawn to highlight the differences between software agents and robotics, and parallel problems from theoretical computer science are identified. This paper further explores robot coalition formation in different practical robotic environments. A heuristic-based coalition formation algorithm from our previous work was extended to operate in precedence ordered cooperative environments. In order to explore coalition formation in competitive environments, the paper also studies the RACHNA system, a market based coalition formation system. Finally, the paper investigates the notion of task preemption for complex multi-robot tasks in random allocation environments.