Coalition structure generation in cooperative games with compact representations

This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well

A Parameterisation of Algorithms for Distributed Constraint Optimisation via Potential Games

This paper introduces a parameterisation of learning algorithms for distributed constraint optimisation problems (DCOPs). This parameterisation encompasses many algorithms developed in both the computer science and game theory literatures. It is built on our insight that when formulated as noncooperative games, DCOPs form a subset of the class of potential games. This result allows us to prove convergence properties of algorithms developed in the computer science literature using game theoretic methods. Furthermore, our parameterisation can assist system designers by making the pros and cons of, and the synergies between, the various DCOP algorithm components clear

Modeling Web Service Selection for Composition as a Distributed Constraint Optimization Problem (DCOP)

During development of a Service-oriented Application, some software pieces could be fulfilled by the connection to Web Services. A list of candidate Web Services could be obtained by making use of any service discovery registry, which are then selected and integrated into the application. However, when it comes to a distributed system, multiple functional and non-functional constraints arise from the interaction between several service requesters and providers, particularly when composing different services. To overcome with such constraints, in this work we propose to model service selection and composition scenarios as Distributed Constraints Optimization Problems (DCOP).We propose different modeling approaches and develop representative examples to be solved through different DCOP algorithms. Also, we analyze the impact of possible extensions to the model in the computability of the problem.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Complexity of Determining Nonemptiness of the Core

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, motivating the agents to abide to 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. However, the computational questions around this constraint 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 paper we define a concise general representation for games in characteristic form that relies on superadditivity, and show that it allows for efficient checking of whether a given outcome is in the core. We then show that determining whether the core is nonempty is $\mathcal{NP}$-complete both with and without transferable utility. We demonstrate that what makes the problem hard in both cases is determining the collaborative possibilities (the set of outcomes possible for the grand coalition), by showing that if these are given, the problem becomes tractable in both cases. However, we then demonstrate that for a hybrid version of the problem, where utility transfer is possible only within the grand coalition, the problem remains $\mathcal{NP}$-complete even when the collaborative possibilities are given