Overlapping Coalitions, Bargaining and Networks

This paper extends the theory of endogenous coalition formation, with complete information and transferable utility, to the overlapping case. We propose a cover function bargaining game which allows the formation of overlapping coalitions at equilibrium. We show the existence of subgame perfect equilibrium and provide an algorithm to compute this equilibrium in the symmetric case. As an application, we establish an interesting link with the formation of networks.Overlapping Coalitions, Cover Function, Bargaining, Symmetric Game, Network

Algorithms for Graph-Constrained Coalition Formation in the Real World

Coalition formation typically involves the coming together of multiple, heterogeneous, agents to achieve both their individual and collective goals. In this paper, we focus on a special case of coalition formation known as Graph-Constrained Coalition Formation (GCCF) whereby a network connecting the agents constrains the formation of coalitions. We focus on this type of problem given that in many real-world applications, agents may be connected by a communication network or only trust certain peers in their social network. We propose a novel representation of this problem based on the concept of edge contraction, which allows us to model the search space induced by the GCCF problem as a rooted tree. Then, we propose an anytime solution algorithm (CFSS), which is particularly efficient when applied to a general class of characteristic functions called $m+a$ functions. Moreover, we show how CFSS can be efficiently parallelised to solve GCCF using a non-redundant partition of the search space. We benchmark CFSS on both synthetic and realistic scenarios, using a real-world dataset consisting of the energy consumption of a large number of households in the UK. Our results show that, in the best case, the serial version of CFSS is 4 orders of magnitude faster than the state of the art, while the parallel version is 9.44 times faster than the serial version on a 12-core machine. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems of agents (i.e., with more than 2700 agents).Comment: Accepted for publication, cite as "in press

Coalition structure generation over graphs

We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph G = (N,E) and a valuation function v : P(N) → R over the subsets of nodes, the problem is to find a partition of N into connected subsets, that maximises the sum of the components values. This problem is generally NP-complete; in particular, it is hard for a defined class of valuation functions which are independent of disconnected members — that is, two nodes have no effect on each others marginal contribution to their vertex separator. Nonetheless, for all such functions we provide bounds on the complexity of coalition structure generation over general and minor free graphs. Our proof is constructive and yields algorithms for solving corresponding instances of the problem. Furthermore, we derive linear time bounds for graphs of bounded treewidth. However, as we show, the problem remains NP-complete for planar graphs, and hence, for any Kk minor free graphs where k ≥ 5. Moreover, a 3-SAT problem with m clauses can be represented by a coalition structure generation problem over a planar graph with O(m2) nodes. Importantly, our hardness result holds for a particular subclass of valuation functions, termed edge sum, where the value of each subset of nodes is simply determined by the sum of given weights of the edges in the induced subgraph

An Algorithm for Distributing Coalitional Value Calculations among Cooperating Agents

The process of forming coalitions of software agents generally requires calculating a value for every possible coalition which indicates how beneficial that coalition would be if it was formed. Now, instead of having a single agent calculate all these values (as is typically the case), it is more efficient to distribute this calculation among the agents, thus using all the computational resources available to the system and avoiding the existence of a single point of failure. Given this, we present a novel algorithm for distributing this calculation among agents in cooperative environments. Specifically, by using our algorithm, each agent is assigned some part of the calculation such that the agents’ shares are exhaustive and disjoint. Moreover, the algorithm is decentralized, requires no communication between the agents, has minimal memory requirements, and can reflect variations in the computational speeds of the agents. To evaluate the effectiveness of our algorithm, we compare it with the only other algorithm available in the literature for distributing the coalitional value calculations (due to Shehory and Kraus). This shows that for the case of 25 agents, the distribution process of our algorithm took less than 0.02% of the time, the values were calculated using 0.000006% of the memory, the calculation redundancy was reduced from 383229848 to 0, and the total number of bytes sent between the agents dropped from 1146989648 to 0 (note that for larger numbers of agents, these improvements become exponentially better)

Cooperation and Competition when Bidding for Complex Projects: Centralized and Decentralized Perspectives

To successfully complete a complex project, be it a construction of an airport or of a backbone IT system, agents (companies or individuals) must form a team having required competences and resources. A team can be formed either by the project issuer based on individual agents' offers (centralized formation); or by the agents themselves (decentralized formation) bidding for a project as a consortium---in that case many feasible teams compete for the contract. We investigate rational strategies of the agents (what salary should they ask? with whom should they team up?). We propose concepts to characterize the stability of the winning teams and study their computational complexity

Multi-Agent Pursuit-Evasion Game Based on Organizational Architecture

Multi-agent coordination mechanisms are frequently used in pursuit-evasion games with the aim of enabling the coalitions of the pursuers and unifying their individual skills to deal with the complex tasks encountered. In this paper, we propose a coalition formation algorithm based on organizational principles and applied to the pursuit-evasion problem. In order to allow the alliances of the pursuers in different pursuit groups, we have used the concepts forming an organizational modeling framework known as YAMAM (Yet Another Multi Agent Model). Specifically, we have used the concepts Agent, Role, Task, and Skill, proposed in this model to develop a coalition formation algorithm to allow the optimal task sharing. To control the pursuers\u27 path planning in the environment as well as their internal development during the pursuit, we have used a Reinforcement learning method (Q-learning). Computer simulations reflect the impact of the proposed techniques

Game Theoretic Approaches to Massive Data Processing in Wireless Networks

Wireless communication networks are becoming highly virtualized with two-layer hierarchies, in which controllers at the upper layer with tasks to achieve can ask a large number of agents at the lower layer to help realize computation, storage, and transmission functions. Through offloading data processing to the agents, the controllers can accomplish otherwise prohibitive big data processing. Incentive mechanisms are needed for the agents to perform the controllers' tasks in order to satisfy the corresponding objectives of controllers and agents. In this article, a hierarchical game framework with fast convergence and scalability is proposed to meet the demand for real-time processing for such situations. Possible future research directions in this emerging area are also discussed

Improving Macrocell - Small Cell Coexistence through Adaptive Interference Draining

The deployment of underlay small base stations (SBSs) is expected to significantly boost the spectrum efficiency and the coverage of next-generation cellular networks. However, the coexistence of SBSs underlaid to an existing macro-cellular network faces important challenges, notably in terms of spectrum sharing and interference management. In this paper, we propose a novel game-theoretic model that enables the SBSs to optimize their transmission rates by making decisions on the resource occupation jointly in the frequency and spatial domains. This procedure, known as interference draining, is performed among cooperative SBSs and allows to drastically reduce the interference experienced by both macro- and small cell users. At the macrocell side, we consider a modified water-filling policy for the power allocation that allows each macrocell user (MUE) to focus the transmissions on the degrees of freedom over which the MUE experiences the best channel and interference conditions. This approach not only represents an effective way to decrease the received interference at the MUEs but also grants the SBSs tier additional transmission opportunities and allows for a more agile interference management. Simulation results show that the proposed approach yields significant gains at both macrocell and small cell tiers, in terms of average achievable rate per user, reaching up to 37%, relative to the non-cooperative case, for a network with 150 MUEs and 200 SBSs