Convex Interval Games

In this paper, convex interval games are introduced and some characterizations are given. Some economic situations leading to convex interval games are discussed. The Weber set and the Shapley value are defined for a suitable class of interval games and their relations with the interval core for convex interval games are established. A square operator is introduced which allows us to obtain interval solutions starting from classical cooperative game theory solutions. It turns out that on the class of convex interval games the square Weber set coincides with the interval core.cooperative games;interval data;convex games;the core;the Weber set;the Shapley value

On 1-convexity and nucleolus of co-insurance games

The situation, in which an enormous risk is insured by a number of insurance companies, is modeled through a cooperative TU game, the so-called co-insurance game, first introduced in Fragnelli and Marina (2004). In this paper we show that a co-insurance game possesses several interesting properties that allow to study the nonemptiness and the structure of the core and to construct an efficient algorithm for computing the nucleolus

On monotonic core allocations for coalitional games whith veto players

We characterize a monotonic core concept defined on the class of veto balanced games. We also discuss what restricted versions of monotonicity are possible when selecting core allocations. We introduce a family of monotonic core concepts for veto balanced games and we show that, in general, the nucleolus per capita is not monotonic.monotonicity, core, nucleolus per capita, TU games

(Average-) convexity of common pool and oligopoly TU-games

The paper studies both the convexity and average-convexity properties for a particular class of cooperative TU-games called common pool games. The common pool situation involves a cost function as well as a (weakly decreasing) average joint production function. Firstly, it is shown that, if the relevant cost function is a linear function, then the common pool games are convex games. The convexity, however, fails whenever cost functions are arbitrary. We present sufficient conditions involving the cost functions (like weakly decreasing marginal costs as well as weakly decreasing average costs) and the average joint production function in order to guarantee the convexity of the common pool game. A similar approach is effective to investigate a relaxation of the convexity property known as the average-convexity property for a cooperative game. An example illustrates that oligopoly games are a special case of common pool games whenever the average joint production function represents an inverse demand function