On the Online Coalition Structure Generation Problem

We consider the online version of the coalition structure generation problem, in which agents, corresponding to the vertices of a graph, appear in an online fashion and have to be partitioned into coalitions by an authority (i.e., an online algorithm). When an agent appears, the algorithm has to decide whether to put the agent into an existing coalition or to create a new one containing, at this moment, only her. The decision is irrevocable. The objective is partitioning agents into coalitions so as to maximize the resulting social welfare that is the sum of all coalition values. We consider two cases for the value of a coalition: (1) the sum of the weights of its edges, and (2) the sum of the weights of its edges divided by its size. Coalition structures appear in a variety of application in AI, multi-agent systems, networks, as well as in social networks, data analysis, computational biology, game theory, and scheduling. For each of the coalition value functions we consider the bounded and unbounded cases depending on whether or not the size of a coalition can exceed a given value α. Furthermore, we consider the case of a limited number of coalitions and various weight functions for the edges, i.e., unrestricted, positive and constant weights. We show tight or nearly tight bounds for the competitive ratio in each case.

Pricing strategies of an oligopolist in federated cloud markets

In this paper, we study how an oligopolist influences the coalition structure in federated cloud markets. Specifically, we use cooperative game theory to model the circumstances under which a cloud provider prefers to join a cloud federation vis-a-vis consider taking a price offer made by an oligopolist. We consider two price offering strategies for an oligopolist: non-adaptive and adaptive. In non-adaptive strategy, an oligopolist makes a price offer to all the cloud providers simultaneously. It can be noted that the oligopolist can buy-out all the cloud providers by making a price offer which is equal to a core allocation and the total price offer made by the oligopolist is equal to the value of the grand coalition. In adaptive strategy, the oligopolist approaches the cloud providers one after another in a sequential manner. We show that by using the adaptive strategy, the oligopolist can buy-out all the cloud providers at a total price offer which is less than that of the non-adaptive strategy.

Testing stability properties in graphical hedonic games

In hedonic games, players form coalitions based on individual preferences over the group of players they could belong to. Several concepts to describe the stability of coalition structures in a game have been proposed and analysed in the literature. However, prior research focuses on algorithms with time complexity that is at least linear in the input size. In the light of very large games that arise from, e.g., social networks and advertising, we initiate the study of sublinear time property testing algorithms for existence and verification problems under several notions of coalition stability in a model of hedonic games represented by graphs with bounded degree. In graph property testing, one shall decide whether a given input has a property (e.g., a game admits a stable coalition structure) or is far from it, i.e., one has to modify at least an $$\epsilon$$ ϵ -fraction of the input (e.g., the game’s preferences) to make it have the property. In particular, we consider verification of perfection, individual rationality, Nash stability, (contractual) individual stability, and core stability. While there is always a Nash-stable coalition structure (which also implies individually stable coalitions), we show that the existence of a perfect coalition structure is not tautological but can be tested. All our testers have one-sided error and time complexity that is independent of the input size.

Coalitional Graph Game of Multi-Hop Clustering in Vehicular Ad-Hoc Networks

Road traffic information can be collected over a vehicular ad-hoc network (VANET) and utilized in many intelligent traffic system applications. A clustering mechanism is used to create a cluster of vehicles to facilitate the data collection from vehicles to road side units (RSUs) acting as sink nodes. Unlike previous works that focus on cluster lifetime or throughput, we propose a coalitional graph game (CGG) technique to form a multi-hop cluster with a largest possible coverage area for a given transmission delay time constraint to economize on the number of RSUs. Vehicles decide to join or leave the coalition based on their individual utility that is a weighted function of number of members in the coalition, relative velocities, distance to sink nodes, and transmission delay toward the sink nodes. The stability of cluster formation is proved by using a discrete-time Markov chain. Our results show that the proposed game model always yields a stable coalition structure that satisfies the objective, and the solutions vary with the weights given to individual components in the utility function.

Min- k -Cut Coalition Structure Generation on Trust-Utility Relationship Graph

Trust relationships have an important effect on coalition formation. In many real scenarios, agents usually cooperate with others in their trusted social networks to form coalitions. Therefore, the trust value between agents should constrain the utility of forming coalitions when cooperating. At the same time, most studies ignore the impact of the number of coalitions in coalition structure. In this paper, the coalition formation of trust-utility relationship in social networks is researched. Each node represents an agent, and the trust-utility networks that connect the agents constrain coalition formation. To solve the task assignment problem, this paper proposes a greedy algorithm which is based on the edge contraction. Under the premise of ensuring the agent’s individually rationality, this algorithm simulates the formation process of coalitions between agents through continuous edge contraction and constrains the number of forming coalitions to k to solve the problem of coalition structure. Finally, the simulation results show that our algorithm has great scalability because of the ability of solving the coalition structure on a large-scale agent set. It can meet the growing demand for data intensive applications in the Internet of things and artificial intelligence era. The quality of the solution is much higher than other algorithms, and the running time is negligible.