American Institute of Mathematical Sciences

Game theory plays an important role in numerous decision-oriented real-life problems. Nowadays, many such problems are basically characterized by various uncertainties. Uncertainties come to happen due to decision makers' collection of data, intuition, assumption, judgement, behaviour, evaluation and lastly, due to the problem itself. Fuzzy concept with membership degree made an initialization towards the treatment of uncertainty, but it was not enough. Intuitionistic fuzzy concept was evolved concerning with both membership and non-membership degrees but failed to express reality more accurately. Then, neutrosophy logic was developed with a new degree in uncertainty, say, indeterminacy degree besides membership and non-membership degrees. Multi-objective optimization is an area of multiple-criteria decision making related with mathematical optimization problems involving more than one objective function to be optimized at the same time. Game theory (matrix game) problems with imprecise, vague information, like neutrosophic, can be formed with multiple objective functions. We develop and analyse a matrix game with multiple objectives, and solve the problem under a single-valued neutrosophic environment in linguistic approach. The main achievement of our study is that we here introduce a problem-oriented example to justify our designed methodologies with a successful real-life implications using linguistic neutrosophic data rather than crisp data as used in previous researches.

A pricing model for the simplest commodity markets is considered. The model describes the behavior of the Order Book, consisting of orders from producers, consumers and speculators. The paper explores the external impact on this model in the form of large operations by new market participants, who at high speeds begin to push forward their orders, for example, first bids and then asks. Such strategies are called swings. This paper investigates a single cycle of one simple trading strategy of the swing type. Found a particular model case of pricing potentiality price relative to swing operation. An example is given, that shows that the simplest commodity markets with producers and consumers have the internal property that they are potentially vulnerable to external influences. The swinging of prices through large purchases and sales leads to systematic profits of the entrants at the expense of the traditional market participants.

We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.

In this paper, we focus on the equal surplus sharing interval solutions for cooperative games, where the set of players are finite and the coalition values are interval numbers. We consider the properties of a class of equal surplus sharing interval solutions consisting of all convex combinations of them. Moreover, an application based on transportation interval situations is given. Finally, we propose three solution concepts, namely the interval Shapley value, ICIS-value and IENSC-value, for this application and these solution concepts are compared.

This paper presents a time-consistent dynamic Shapley value imputation for a class of differential network games. A novel form for measuring the worth of coalitions – named as cooperative-trajectory characteristic function – is developed for the Shapley value imputation. This new class of characteristic functions is evaluated along the cooperative trajectory. It measures the worth of coalitions under the process of cooperation instead of under min-max confrontation or the Nash non-cooperative stance. The resultant dynamic Shapley value imputation yields a new cooperative solution in differential network games.