We join the goals of two giant and related fields research in group decision-making that have historically had little contact: fair division, efficient mechanism design with monetary payments. To do this we adopt standard paradigm where utility is assumed to be quasilinear thus transferable across agents. generalize traditional binary criteria envy-freeness, proportionality, efficiency (welfare...

‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎

This paper deals with bimatrix games in uncertainty environment based on several types of ordering, which Maeda proposed. But Maeda’s models was just made based on symmetrical triangle fuzzy variable. In this paper, we generalized Maeda’s model to the non-symmetrical environment. In other words, we investigated the fuzzy bimatrix games based on nonsymmetrical L-R fuzzy variables. Then the pseud...

the intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by atanassov in 1983. the aim of this paper is to develop an effective methodology for solving matrix games with payoffs of atanassov’s triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concepts and ranking order relations of atanassov’s tifns are defined. a pair of bi-object...

The objective of this paper is to develop matrix games with pay-offs of triangular hesitant fuzzy elements (THFEs). To solve such games, a new methodology has been derived based on the notion of weighted average operator and score function of THFEs. Firstly, we formulate two non-linear programming problems with THFEs. Then applying the score function of THFEs, we transform these two problems in...

In this paper, we give a further discussion on the core solution for cooperative games with fuzzy payoffs. Some notions and results from classical games are extended to fuzzy cooperative games. Using an example, we point out that the theorem about the nonempty of I-core proposed in 2008 was not sufficient. Furthermore, the equivalence relation between balanced game and nonempty core, which play...

In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache’s axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value ...

This paper presents a dynamic model of endogenous coalition formation in cooperative games with transferable utility. The players are boundedly rational. At each time step, a player decides which of the existing coalitions to join, and demands a payo . These decisions are determined by a best{reply rule, given the coalition structure and allocation in the previous period. Further, the players e...

In the context of cooperative games with transferable utility, an inclusive collusion grants each colluding player access to resources of all colluding players and therefore transforms a given game. Inclusive collusion neutrality requires that no group of players can change their total payo↵ with an inclusive collusion. Assuming that collusion formation is governed by a network defined over pla...