Allocation rules incorporating interval uncertainty

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.allocation rules, bankruptcy, interval uncertainty

Convex games versus clan games

In this paper we provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. We show that a "dualize and restrict" procedure transforms total clan games with zero worth for the clan into monotonic convex games. Furthermore, each monotonic convex game generates a total clan game with zero worth for the clan by a "dualize and extend" procedure. These procedures are also useful for relating core elements and elements of the Weber set of the corresponding games.convex games, core, dual games, marginal games, total clan games, Weber set

Bankruptcy problems with interval uncertainty

In this paper, bankruptcy situations with interval data are studied. Two classical bankruptcy rules, namely the proportional rule and the rights-egalitarian rule, are extended to the interval setting. It turns out that these bankruptcy interval rules generate elements in the interval core of a related cooperative interval game.

Shapley-like values for interval bankruptcy games

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.

Convex games, clan games, and their marginal games

We provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. As it turns out, a cooperative game is convex if and only if all its marginal games are superadditive, and a monotonic game satisfying the veto player property with respect to the members of a coalition C is a total clan game (with clan C) if and only if all its C-based marginal games are subadditive

Some Characterizations of Convex Interval Games

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.Cooperative interval games, convex games, big boss games, superadditive games, marginal games, exact games

Convex games, clan games, and their marginal games

We provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. As it turns out, a cooperative game is convex if and only if all its marginal games are superadditive, and a monotonic game satisfying the veto player property with respect to the members of a coalition C is a total clan game (with clan C) if and only if all its C-based marginal games are superadditive.characterization, convex games, marginal games, subadditive games, superadditive games, total clan games

Cooperation in Dividing the Cake

This paper defines models of cooperation among players partitioning 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 cooperating 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 division.This paper defines models of cooperation among players partitioning 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 cooperating 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 division.Refereed Working Papers / of international relevanc

Convex Interval Games

Convex interval games are introduced and 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. The notion of population monotonic interval allocation scheme (pmias) in the interval setting is introduced and it is proved that each element of the Weber set of a convex interval game is extendable to such a pmias. A square operator is introduced which allows us to obtain interval solutions starting from the corresponding 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