A Logic-Based Representation for Coalitional Games with Externalities

We consider the issue of representing coalitional games in multiagent systems that exhibit externalities from coalition formation, i.e., systems in which the gain from forming a coalition may be affected by the formation of other co-existing coalitions. Although externalities play a key role in many real-life situations, very little attention has been given to this issue in the multi-agent system literature, especially with regard to the computational aspects involved. To this end, we propose a new representation which, in the spirit of Ieong and Shoham [9], is based on Boolean expressions. The idea behind our representation is to construct much richer expressions that allow for capturing externalities induced upon coalitions. We show that the new representation is fully expressive, at least as concise as the conventional partition function game representation and, for many games, exponentially more concise. We evaluate the efficiency of our new representation by considering the problem of computing the Extended and Generalized Shapley value, a powerful extension of the conventional Shapley value to games with externalities. We show that by using our new representation, the Extended and Generalized Shapley value, which has not been studied in the computer science literature to date, can be computed in time linear in the size of the input

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

Computational Aspects of Extending the Shapley Value to Coalitional Games with Externalities

Until recently, computational aspects of the Shapley value were only studied under the assumption that there are no externalities from coalition formation, i.e., that the value of any coalition is independent of other coalitions in the system. However, externalities play a key role in many real-life situations and have been extensively studied in the game-theoretic and economic literature. In this paper, we consider the issue of computing extensions of the Shapley value to coalitional games with externalities proposed by Myerson [21], Pham Do and Norde [23], and McQuillin [17]. To facilitate efficient computation of these extensions, we propose a new representation for coalitional games with externalities, which is based on weighted logical expressions. We demonstrate that this representation is fully expressive and, sometimes, exponentially more concise than the conventional partition function game model. Furthermore, it allows us to compute the aforementioned extensions of the Shapley value in time linear in the size of the input

Heuristic methods for coalition structure generation

The Coalition Structure Generation (CSG) problem requires finding an optimal partition of a set of n agents. An optimal partition means one that maximizes global welfare. Computing an optimal coalition structure is computationally hard especially when there are externalities, i.e., when the worth of a coalition is dependent on the organisation of agents outside the coalition. A number of algorithms were previously proposed to solve the CSG problem but most of these methods were designed for systems without externalities. Very little attention has been paid to finding optimal coalition structures in the presence of externalities, although externalities are a key feature of many real world multiagent systems. Moreover, the existing methods, being non-heuristic, have exponential time complexity which means that they are infeasible for any but systems comprised of a small number of agents. The aim of this research is to develop effective heuristic methods for finding optimal coalition structures in systems with externalities, where time taken to find a solution is more important than the quality of the solution. To this end, four different heuristics methods namely tabu search, simulated annealing, ant colony search and particle swarm optimisation are explored. In particular, neighbourhood operators were devised for the effective exploration of the search space and a compact representation method was formulated for storing details about the multiagent system. Using these, the heuristic methods were devised and their performance was evaluated extensively for a wide range of input data

A Self-Tuning procedure for resource management in InterCloud Computing

Beijing Key Laboratory on Integration and Analysis of Large-scale Stream Data, College of Computer Science, North China University of Technology, Beijing, China The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.InterCloud Computing is a new cloud paradigm designed to guarantee service quality or performance and availability of on-demand resources. InterCloud enables cloud interoperability by promoting the interworking of cloud systems from different cloud providers using standard interfacing. Resource management in InterCloud, considered as an important functional requirement, has not attracted commensurate research attention. The focus of this paper is to propose a Software Cybernetic approach, in the form of an adaptive control framework, for efficient management of shared resources in peer-to-peer InterCloud computing. This research effort adopts cooperative game theory to model resource management in InterCloud. The space of cooperative arrangements (resource sharing) between the participant cloud systems is presented by using Integer Partitioning to characterise the worst case communication complexity in peer to peer InterCloud. Essentially, this paper presents an Integer partition based anytime algorithm as an optimal cost solution to the bi-objective optimisation problem in resource management, anchored principally on practical trade-off between the desired performance (quality of service) and communication complexity of collaborating resource clouds

Computing optimal coalition structures in polynomial time

The optimal coalition structure determination problem is in general computationally hard. In this article, we identify some problem instances for which the space of possible coalition structures has a certain form and constructively prove that the problem is polynomial time solvable. Specifically, we consider games with an ordering over the players and introduce a distance metric for measuring the distance between any two structures. In terms of this metric, we define the property of monotonicity, meaning that coalition structures closer to the optimal, as measured by the metric, have higher value than those further away. Similarly, quasi-monotonicity means that part of the space of coalition structures is monotonic, while part of it is non-monotonic. (Quasi)-monotonicity is a property that can be satisfied by coalition games in characteristic function form and also those in partition function form. For a setting with a monotonic value function and a known player ordering, we prove that the optimal coalition structure determination problem is polynomial time solvable and devise such an algorithm using a greedy approach. We extend this algorithm to quasi-monotonic value functions and demonstrate how its time complexity improves from exponential to polynomial as the degree of monotonicity of the value function increases. We go further and consider a setting in which the value function is monotonic and an ordering over the players is known to exist but ordering itself is unknown. For this setting too, we prove that the coalition structure determination problem is polynomial time solvable and devise such an algorithm

Heuristic methods for optimal coalition structure generation

The problem of finding the optimal coalition structure arises frequently in multiagent systems. Heuristic approaches for solving this problem are needed because of its computational complexity. This paper studies two such approaches: tabu search and simulated annealing. Through simulations we show that tabu search generates better quality solutions than simulated annealing for coalition games in characteristic function form and those in partition function form

Impure Public Goods and Technological Interdependencies

Impure public goods represent an important group of goods. Almost every public good exerts not only effects which are public to all but also effects which are private to the producer of this good. What is often omitted in the analysis of impure public goods is the fact that – regularly – these private effects can also be generated independently of the public good. In our analysis we focus on the effects alternative technologies – independently generating the private effects of the public good – may have on the provision of impure public goods. After the investigation in an analytical impure public good model, we numerically simulate the effects of alternative technologies in a parameterized model for climate policy in Germany.Impure public goods, Climate policy, Rationing

The Economics of Local Tourist Systems

In this paper we analyse the Local Tourist System (LTS) as a particular case of Marshallian Industrial District. The LTS allows the identification of more effective policy tools for managing tourism. First, through the concept of LTS, the policy maker can take into account the complexity of tourism, characterised by a strong heterogeneity of goods, services and subjects involved; second, LTS helps promote a stronger co-ordination between the public and the private sector, by identifying a homogeneous territory and recognising its importance in tourists' decisions; third, through the LTS the policymaker can analyze the externalities and promotes the idea of collaborating networks in a context of local development. In the LTS framework, the anticommon problem can be analysed and contrasted. As the tourist has to buy different but intertwined goods which compose the holiday package, the failure in one of the markets can lead to the overall failure of the package. A LTS policy has to: i) co-ordinate the price policy of the different firms supplying “single components” of the tourist product; ii) fix the price of the whole product; iii) impute a price to each component. We demonstrate that, through price policy co-ordination and under general conditions, the LTS can increase the size of tourism and the firms’ profits, thereby reaching a more effective and efficient target in tourism policy. The recent introduction of LTS in the Italian legislation can be seen as a positive attempt of improving co-ordination in a complex sector such as tourism.Local tourist systems, Tourism policy

The Computational Difficulty of Bribery in Qualitative Coalitional Games

Qualitative coalitional games (QCG) are representations of coalitional games in which self interested agents, each with their own individual goals, group together in order to achieve a set of goals which satisfy all the agents within that group. In such a representation, it is the strategy of the agents to find the best coalition to join. Previous work into QCGs has investigated the computational complexity of determining which is the best coalition to join. We plan to expand on this work by investigating the computational complexity of computing agent power in QCGs as well as by showing that insincere strategies, particularly bribery, are possible when the envy-freeness assumption is removed but that it is computationally difficult to identify the best agents to bribe.Bribery, Coalition Formation, Computational Complexity