Cooperative Games with Overlapping Coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions--or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

Computational Intelligence Inspired Data Delivery for Vehicle-to-Roadside Communications

We propose a vehicle-to-roadside communication protocol based on distributed clustering where a coalitional game approach is used to stimulate the vehicles to join a cluster, and a fuzzy logic algorithm is employed to generate stable clusters by considering multiple metrics of vehicle velocity, moving pattern, and signal qualities between vehicles. A reinforcement learning algorithm with game theory based reward allocation is employed to guide each vehicle to select the route that can maximize the whole network performance. The protocol is integrated with a multi-hop data delivery virtualization scheme that works on the top of the transport layer and provides high performance for multi-hop end-to-end data transmissions. We conduct realistic computer simulations to show the performance advantage of the protocol over other approaches

Fuzzy coalitional structures (alternatives)

The uncertainty of expectations and vagueness of the interests belong to natural components of cooperative situations, in general. Therefore, some kind of formalization of uncertainty and vagueness should be included in realistic models of cooperative behaviour. This paper attempts to contribute to the endeavour of designing a universal model of vagueness in cooperative situations. Namely, some initial auxiliary steps toward the development of such a model are described. We use the concept of fuzzy coalitions suggested in [1], discuss the concepts of superadditivity and convexity, and introduce a concept of the coalitional structure of fuzzy coalitions. The first version of this paper [10] was presented at the Czech-Japan Seminar in Valtice 2003. It was obvious that the roots of some open questions can be found in the concept of superadditivity (with consequences on some other related concepts), which deserve more attention. This version of the paper extends the previous one by discussion of alternative approaches to this topic

Cooperative games with overlapping coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

On the set of imputations induced by the k-additive core

An extension to the classical notion of core is the notion of $k$-additive core, that is, the set of $k$-additive games which dominate a given game, where a $k$-additive game has its Möbius transform (or Harsanyi dividends) vanishing for subsets of more than $k$ elements. Therefore, the 1-additive core coincides with the classical core. The advantages of the $k$-additive core is that it is never empty once $k\geq 2$, and that it preserves the idea of coalitional rationality. However, it produces $k$-imputations, that is, imputations on individuals and coalitions of at most $k$ individuals, instead of a classical imputation. Therefore one needs to derive a classical imputation from a $k$-order imputation by a so-called sharing rule. The paper investigates what set of imputations the $k$-additive core can produce from a given sharing rule.

Collaborative Models for Supply Networks Coordination and Healthcare Consolidation

This work discusses the collaboration framework among different members of two complex systems: supply networks and consolidated healthcare systems. Although existing literature advocates the notion of strategic partnership/cooperation in both supply networks and healthcare systems, there is a dearth of studies quantitatively analyzing the scope of cooperation among the members and its benefit on the global performance. Hence, the first part of this dissertation discusses about two-echelon supply networks and studies the coordination of buyers and suppliers for multi-period procurement process. Viewing the issue from the same angel, the second part studies the coordination framework of hospitals for consolidated healthcare service delivery. Realizing the dynamic nature of information flow and the conflicting objectives of members in supply networks, a two-tier coordination mechanism among buyers and suppliers is modeled. The process begins with the intelligent matching of buyers and suppliers based on the similarity of users profiles. Then, a coordination mechanism for long-term agreements among buyers and suppliers is proposed. The proposed mechanism introduces the importance of strategic buyers for suppliers in modeling and decision making process. To enhance the network utilization, we examine a further collaboration among suppliers where cooperation incurs both cost and benefit. Coalitional game theory is utilized to model suppliers\u27 coalition formation. The efficiency of the proposed approaches is evaluated through simulation studies. We then revisit the common issue, the co-existence of partnership and conflict objectives of members, for consolidated healthcare systems and study the coordination of hospitals such that there is a central referral system to facilitate patients transfer. We consider three main players including physicians, hospitals managers, and the referral system. As a consequence, the interaction within these players will shape the coordinating scheme to improve the overall system performance. To come up with the incentive scheme for physicians and aligning hospitals activities, we define a multi-objective mathematical model and obtain optimal transfer pattern. Using optimal solutions as a baseline, a cooperative game between physicians and the central referral system is defined to coordinate decisions toward system optimality. The efficiency of the proposed approach is examined via a case study

The power index at infinity: Weighted voting in sequential infinite anonymous games

After we describe the waiting queue problem, we identify a partially observable 2n+1-player voting game with only one pivotal player; the player at the n-1 order. Given the simplest rule of heterogeneity presented in this paper, we show that for any infinite sequential voting game of size 2n+1, a power index of size n is a good approximation of the power index at infinity, and it is difficult to achieve. Moreover, we show that the collective utility value of a coalition for a partially observable anonymous game given an equal distribution of weights is n²+n. This formula is developed for infinite sequential anonymous games using a stochastic process that yields a utility function in terms of the probability of the sequence and voting outcome of the coalition. Evidence from Wikidata editing sequences is presented and the results are compared for 10 coalitions