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Games where players' payoffs are given by intervals, instead of scalars, provide a conceptually attractive framework to account for uncertainty and vagueness in decision-making processes. In a cooperative game, one needs to determine the characteristic function values for all possible coalitions. In this paper, we extend the classical $ \alpha $ and $ \beta $ characteristic functions (CFs), initially defined for scalar payoffs, to cooperative interval games. Both characteristic functions are based on a solution of zero-sum interval games with the coalition being the maximizer player and the anti-coalition the minimizer player. We propose an algorithm to define the interval values of a cooperative game in the form of $ \alpha $ and $ \beta $ CFs and illustrate its use on an example with three players. Further, we discuss some properties of cooperative interval games and calculate an interval Shapley value. As expected, different characteristic functions lead to different Shapley values. [ABSTRACT FROM AUTHOR]

The social arrangement of organizations determines the potential possibilities of all group of agents in several economic and Operations Research (OR) situations. In this paper, a class of cooperative games in which agents with potential individual possibilities are connected via a hierarchy within an organization is studied. The leader, the agent, and any intermediate agents in the specified hierarchy constitute an important group refering to a peer group and form peer group situations. We consider uncertanty in payoffs in peer group situations. In the sequel peer group settings with fuzzy uncertainty are proposed. Further the associated games are modeled and some game-theoretical solution concepts are provided Futhermore, an application related with an auction situation is given. Finally, we conclude with some remarks and future work. [ABSTRACT FROM AUTHOR]

Cost sharing problems can arise from situations in which some service is provided to a variety of different customers who differ in the amount or type of service they need. One can think of and airports computers, telephones. This paper studies an airport problem which is concerned with the cost sharing of an airstrip between airplanes assuming that one airstrip is sufficient to serve all airplanes. Each airplane needs an airstrip whose length can be different across airplanes. Also, it is important how should the cost of each airstrip be shared among airplanes. The purpose of the present paper is to give an axiomatic characterization of the Baker-Thompson rule by using grey calculus. Further, it is shown that each of our main axioms (population fairness, smallest-cost consistency and balanced population impact) together with various combina tions of our minor axioms characterizes the best-known rule for the problem, namely the Baker-Thompson rule. Finally, it is demonstrated that the grey Shapley value of airport game and the grey Baker-Thompson rule coincides. [ABSTRACT FROM AUTHOR]

The job scheduling problem is a notoriously difficult problem in combinatorial optimization and Operational Research. In this study, we handle the job scheduling problem by using a cooperative game theoretical approach. In the sequel, sequencing situations arising grom grey uncertainty are considered. Cooperative grey game theory is applied to analyze these situations. Further, grey sequencing games are constructed and grey equal gain splitting (GEGS) rule is introduced. It is shown that cooperative grey games are convex. An application is given based on Priority Based Scheduling Algorithm. The paper ends with a conclusion. [ABSTRACT FROM AUTHOR]

The aim of this study is to provide a mathematical framework for studying node cooperation, and to define strategies leading to optimal node behaviour in ad hoc networks. In this study we show time performances of three different methods, namely, Dijkstra's algorithm, Dijkstra's algorithm with battery times and cooperative flow game algorithm constructed from a flow network model. There are two main outcomes of this study regarding the shortest path problem which is that of finding a path of minimum length between two distinct vertices in a network. The first one finds out which method gives better results in terms of time while finding the shortest path, the second one considers the battery life of wireless devices on the network to determine the remaining nodes on the network. Further, optimization performances of the methods are examined in finding the shortest path problem. The study shows that the battery times play an important role in network routing and more devices provided to keep the network. To view the time performance analysis of the methods MATLAB is used. Also, considering the cooperation between the nodes, it is envisaged that using cooperative game theory brings a new approach to network traffic engineering and routing methods. [ABSTRACT FROM AUTHOR]