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

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

A service is produced for a set of agents. The service is binary, each agent either receives service or not, and the total cost of service is a submodular function of the set receiving service. We investigate strategyproof mechanisms that elicit individual willingness to pay, decide who is served, and then share the cost among them. If such a mechanism is budget balanced (covers cost exactly), it cannot be efficient (serve the surplus maximizing set of users) and vice-versa. We characterize the rich family of budget balanced and group strategyproof mechanisms; they correspond to the family of cost sharing formulae where an agent's cost share does not decrease when the set of users expand. The mechanism associated with the Shapley value cost sharing formula is characterized by the property that its worst welfare loss is minimal. When we require efficiency rather than budget balance -- the more common route in the literature -- we find that there is a single Clarke-Groves mech...

A Dissertation Presented by TUOMAS W. SANDHOLM

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

We study k-resilient Nash equilibria, joint strategies where no member of a coalition C of size up to k can do better, even if the whole coalition defects. We show that such k-resilient Nash equilibria exist for secret sharing and multiparty computation, provided that players prefer to get the information than not to get it. Our results hold even if there are only 2 players, so we can do multiparty computation with only two rational agents. We extend our results so that they hold even in the presence of up to t players with “unexpected” utilities. Finally, we show that our techniques can be used to simulate games with mediators by games without mediators. Categories and Subject Descriptors: F.0 [Theory of Computation]: General.

A strong equilibrium (Aumann 1959) is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy to be the ratio of the worst case strong equilibrium to the social optimum. In contrast to the traditional price of anarchy, which quantifies the loss incurred due to both selfishness and lack of coordination, the strong price of anarchy isolates the loss originated from selfishness from that obtained due to lack of coordination. We study the strong price of anarchy in two settings, one of job scheduling and the other of network creation. In the job scheduling game we show that for unrelated machines the strong price of anarchy can be bounded as a function of the number of machines and the size of the coalition. For the network creation game we show that the strong price of anarchy is at most 2. In both cases we show that a strong equilibrium always exists, except for a well defined subset of network creation games. ∗ This work was supported in part by the IST Programme of the European Community, under the PASCAL

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We present, to our knowledge, the first mixed integer program (MIP) formulations for finding Nash equilibria in games (specifically, two-player normal form games). We study different design dimensions of search algorithms that are based on those formulations. Our MIP Nash algorithm outperforms Lemke-Howson but not Porter-Nudelman-Shoham (PNS) on GAMUT data. We argue why experiments should also be conducted on games with equilibria with medium-sized supports only, and present a methodology for generating such games. On such games MIP Nash drastically outperforms PNS but not Lemke-Howson. Certain MIP Nash formulations also yield anytime algorithms for #-equilibrium, with provable bounds. Another advantage of MIP Nash is that it can be used to find an optimal equilibrium (according to various objectives). The prior algorithms can be extended to that setting, but they are orders of magnitude slower.