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.

In this paper, we will analyze the phenomenon of strategic cooperation between companies competing with each other so far. The analysis will concern the real situation of establishing a strategic alliance between companies. The analysis will consist in assessing the effects of cooperation for each of the companies, depending on whether and in what composition the companies would decide to cooperate. For the analysis, we will use a mathematical model of a cooperative game with fuzzy characteristic functions. Finally, we propose fuzzy interval solutions are a timely extension to classical game theoretic solutions.

Purpose: This paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. This means that one observes a lower and an upper bound of the considered coalitions. This is very important, for example, from a computational and algorithmic viewpoint. The authors notice that the approach is general, since the characteristic function fuzzy interval values may result from solving general optimization problems.Design/methodology/approach: This paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. A situation in which a finite set of players can obtain certain fuzzy payoffs by cooperation can be described by a cooperative fuzzy interval game.Findings: In this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty.Originality/value: In this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty. Examples of such solutions are the centre-of-gravity of the imputation-set value, shortly denoted by CIS value, egalitarian non-separable contribution value, shortly denoted by ENSC value and the equal division solution. Further, the authors discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS value, the ENSC value and the equal division solution. The authors provide several characterizations of this class of solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class.

The allocation problem of rewards/costs is a basic question for players namely individuals and companies that planning cooperation under uncertainty. The involvement of uncertainty in cooperative game theory is motivated by the real world where noise in observation and experimental design, incomplete information and further vagueness in preference structures and decision-making play an important role. In this paper we extend cooperative bubbly games to cooperative fuzzy bubbly games, where the worth of each coalition is a fuzzy bubble instead of an interval. Further, we introduce a set-valued concept called the fuzzy bubbly core. Finally, some results on fuzzy bubbly core are given.