Probability Bounds for Overlapping Coalition Formation

In this work, we provide novel methods which benefit from obtained probability bounds for assessing the ability of teams of agents to accomplish coalitional tasks. To this end, our first method is based on an improvement of the Paley-Zygmund inequality, while the second and the third ones are devised based on manipulations of the two-sided Chebyshev’s inequality and the Hoeffding’s inequality, respectively. Agents have no knowledge of the amount of resources others possess; and hold private Bayesian beliefs regarding the potential resource investment of every other agent. Our methods allow agents to demand that certain confidence levels are reached, regarding the resource contributions of the various coalitions. In order to tackle real-world scenarios, we allow agents to form overlapping coalitions, so that one can simultaneously be part of a number of coalitions. We thus present a protocol for iterated overlapping coalition formation (OCF), through which agents can complete tasks that grant them utility. Agents lie on a social network and their distance affects their likelihood of cooperation towards the completion of a task. We confirm our methods’ effectiveness by testing them on both a random graph of 300 nodes and a real-world social network of 4039 nodes.

The First ‘General Chapter’ of Benedictine Abbots (1131) Reconsidered

This paper reconsiders the first ‘General Chapter’ of Benedictine abbots (late 1131). To explain the timing and circumstances of this event, previous scholarship mostly referred to the influence of the Cistercians on reformist groups within ‘traditional’ monasticism. A closer look at the primary evidence reveals how the first General Chapter needs to be framed against the activities of overlapping coalitions of ecclesiastical and secular agents pursuing various political, ideological and institutional interests. It also allows the causes of the ensuing dispute with the Cluniacs to be established more securely, and provides new insights into contemporary usages of statutes and the semantics of the word ‘ordo’.

USING THE ASPIRATION CORE TO PREDICT COALITION FORMATION

This work uses the defining principles of the core solution concept to determine not only payoffs but also coalition formation. Given a cooperative transferable utility (TU) game, we propose two noncooperative procedures that in equilibrium deliver a natural and nonempty core extension, the aspiration core, together with the supporting coalitions it implies. As expected, if the cooperative game is balanced, the grand coalition forms. However, if the core is empty, other coalitions arise. Following the aspiration literature, not only partitions but also overlapping coalition configurations are allowed. Our procedures interpret this fact in different ways. The first game allows players to participate with a fraction of their time in more than one coalition, while the second assigns probabilities to the formation of potentially overlapping coalitions. We use the strong Nash and subgame perfect Nash equilibrium concepts.