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This paper deals with a constrained egalitarian solution for convex multi-choice games named the d value. It is proved that the d value of a convex multi-choice game belongs to the precore, Lorenz dominates each other element of the precore and possesses a population monotonicity property regarding players’ participation levels. Furthermore, an axiomatic characterization is given where a specific consistency property plays an important role.

This paper introduces and studies a class of cooperative interval games suitable to model market situations with two corners where players face interval uncertainty regarding the outcome of cooperation. In one corner there is a powerful player called the big boss; the other corner contains players that need the big boss to benefit from cooperation. Various characterizations of big boss interval games are given. The interval core of a big boss interval game is explicitly described, bi-monotonic allocation schemes using interval core elements are introduced, and it is shown that each element of the interval core of a big boss interval game is extendable to such a scheme. Two value-type interval solution concepts are defined on the class of big boss interval games which generate for each such game the same interval core allocation which is extendable to a bi-monotonic interval allocation scheme.

Uncertainty accompanies almost every situation in our lives and it influences our decisions. On many occasions uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our (collaborative) actions, i.e., payoffs lie in some intervals. Cooperative interval games have been proved useful for solving reward/cost sharing problems in situations with interval data in a cooperative environment. In this paper we propose two procedures for cooperative interval games. Both transform an interval allocation, i.e., a payoff vector whose components are compact intervals of real numbers, into a payoff vector (whose components are real numbers) when the value of the grand coalition becomes known (at once or in multiple stages). The research question addressed here is: How to determine for each player his/her/its payoff generated by cooperation within the grand coalition – in the promised range of payoffs to establish such cooperation – after the uncertainty on the payoff for the grand coalition is resolved? This question is an important one that deserves attention both in the literature and in game practice.

We give a non-cooperative and an axiomatic characterization of the Average Lexicographic value (AL-value) on the class of balanced games. The AL-value is a single-valued solution for balanced TU-games. It is defined as the average of lexicographic maximum of the core of the game with respect to all orders on the player set, and it can be seen as a core selection based on the priority orders on the players. In both of our characterizations of the AL-value, a consistency property which we call average consistency plays an important role, and the property is obtained by the consistency property à la Davis and Maschler of the lexicographic vectors with respect to any order of players.

In this paper, we consider market situations with two corners. One corner consists of a group of powerful agents with yes-or-no choices and clan behavior. The other corner consists of non-powerful agents with multi-choices regarding the extent at which cooperation with the clan can be achieved. Multi-choice clan games arise from such market situations. The focus is on the analysis of the core of multi-choice clan games. Several characterizations of multi-choice clan games by the shape of the core are given, and the connection between the convexity of a multi-choice clan game and the stability of its core is studied.

This paper deals with the research area of cooperative interval games arising from airport situations with interval data. The major topic of the paper is to present and identify the interval Baker–Thompson rule.

This paper deals with cooperative fuzzy games arising from two economic situations: a linear production situation and a labor-time availability situation. In both economic situations we derive cooperative fuzzy games and study conditions for nonemptiness of Aubin's core. Also, relations between reasona-ble (stable) payoff schemes for the economic situations and core elements of the related cooperative fuzzy games are studied

In this paper interval bankruptcy games arising from bankruptcy situations with interval claims are introduced. For this class of cooperative games two (marginal-based) Shapley-like values are considered and the relation between them is studied.

This chapter examines several monotonicity properties of value-type interval solutions on the class of convex interval games and focuses on the Dutta–Ray (DR) solution for such games. Well-known properties for the classical DR solution are extended to the interval setting. In particular, it is proved that the interval DR solution of a convex interval game belongs to the interval core of that game and Lorenz dominates each other interval core element. Consistency properties of the interval DR solution in the sense of Davis–Maschler and of Hart–Mas-Colell are verified. An axiomatic characterization of the interval DR solution on the class of convex interval games with the help of bilateral Hart–Mas-Colell consistency and the constrained egalitarianism for two-person interval games is given.

This paper concentrates on the management of delayed projects charged with penalty costs and of expedited projects rewarded with bonuses, based on an activity graph description of the projects. We propose a two-stage heuristic procedure to assist project managers to determine “fair” shares of penalties or compensations for agents involved when information regarding the project’s schedule and its actual execution is available. Incentives for better performance play a key role in this procedure, which combines a “bonus-malus” approach with a rationing approach. In the first stage, activities’ deviations from the schedule are computed using heuristic algorithms which implement incentives for better performance according to two alternative scenarios. In the second stage, the deviations of activities computed according to the chosen scenario are adjusted using well-known rules from the literature on rationing problems. A new family of compensations-penalties solutions, called Mutual Help Solutions, is introduced and illustrated.

This paper defines models of cooperation among players partition- ing a completely divisible good (such as a cake or a piece of land). The novelty of our approach lies in the players' ability to form coalitions before the actual division of the good with the aim to maximize the average utility of the coalition. A social welfare function which takes into account coalitions drives the division. In addition, we derive a cooperative game which measures the performance of each coalition. This game is compared with the game in which players start cooper- ating only after the good has been portioned and has been allocated among the players. We show that a modified version of the game played before the division outperforms the game played after the di- vision.

This paper provides several answers to the question “How to cope with rationing problems with interval data?” Interval allocation rules which are efficient and reasonable are designed, with special attention to interval bankruptcy problems with standard claims and allocation rules incorporating the interval uncertainty of the estate.

This paper focuses on two characterizations of convex interval games using the notions of superadditivity and exactness, respectively. We also relate big boss interval games with concave interval games and obtain characterizations of big boss interval games in terms of subadditivity and exactness.