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.

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

Cores and Stable Sets for Interval-Valued Games

In this paper, interval-type solution concepts for interval-valued cooperative games like the interval core, the interval dominance core and stable sets are introduced and studied. The notion of I-balancedness is introduced, and it is proved that the interval core of an interval-valued cooperative game is nonempty if and only if the game is I-balanced. Relations between the interval core, the dominance core and stable sets of an interval-valued game are established.cooperative games;interval games;the core;the dominance core;stable sets

Cooperation under Interval Uncertainty

Classification: JEL code C71Cooperative game theory;Interval uncertainty;Core;Value;Balancedness

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

Sequencing Interval Situations and Related Games

In this paper we consider one-machine sequencing situations with interval data. We present different possible scenarioes and extend classical results on well known rules and on sequencing games to the interval setting.cooperative games;interval data;sequencing situations;convex games