Convex Congestion Network Problems

This paper analyzes convex congestion network problems.It is shown that for network problems with convex congestion costs, an algorithm based on a shortest path algorithm, can be used to find an optimal network for any coalition. Furthermore an easy way of determining if a given network is optimal is provided.game theory;cooperative games;algorithm

Processing Games with Shared Interest

A generalization of processing problems with restricted capacities is introduced.In a processing problem there is a finite set of jobs, each requiring a specific amount of effort to be completed, whose costs depend linearly on their completion times.The new aspect is that players have interest in all jobs. The corresponding cooperative game of this generalization is proved to be totally balanced.Processing games;scheduling;core allocation

A Stroll with Alexia

This paper revisits the Alexia value, a recent solution concept for cooperative transferable utility games. We introduce the dual Alexia value and show that it coincides with the Alexia value for several classes of games. We demonstrate the importance of the notion of compromise stability for characterizing the Alexia value.Alexia value;dual Alexia value;compromise stability;bankruptcy

Characterizing Compromise Stability of Games Using Larginal Vectors

The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an order of the players and describes the efficient payoff vector giving the first players in the order their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. In this paper we describe two ways of characterizing sets of larginal vectors that satisfy the condition that if every larginal vector of the set is a core element, then the game is compromise stable. The first characterization of these sets is based on a neighbor argument on orders of the players. The second one uses combinatorial and matching arguments and leads to a complete characterization of these sets. We find characterizing sets of minimum cardinality, a closed formula for the minimum number of orders in these sets, and a partition of the set of all orders in which each element of the partition is a minimum characterizing set.Core;core cover;larginal vectors;matchings

A Concede-and-Divide Rule for Bankruptcy Problems

The concede-and-divide rule is a basic solution for bankruptcy problems with two claimants.An extension of the concede-and-divide rule to bankruptcy problems with more than two claimants is provided.This extension not only uses the concede-and-divide principle in its procedural definition, but also preserves the main properties of the concede-and-divide rule.Bankruptcy problems;concede-and-divide rule

On a Compromise Social Choice Correspondence

This paper analyzes the compromise social choice correspondence derived from the F-value of digraph games.Among other things monotonicity of this correspondence is shownsocial choice;games;t-value

Processing Games with Restricted Capacities

This paper analyzes processing problems and related cooperative games.In a processing problem there is a finite set of jobs, each requiring a specific amount of effort to be completed, whose costs depend linearly on their completion times.There are no restrictions whatsoever on the processing schedule.The main feature of the model is a capacity restriction, i.e., there is a maximum amount of effort per time unit available for handling jobs.Assigning to each job a player and letting each player have an individual capacity for handling jobs, each coalition of cooperating players in fact faces a processing problem with the coalitional capacity being the sum of the individual capacities of the members.The corresponding processing game summarizes the minimal joint costs for every coalition.It turns out that processing games are totally balanced.An explicit core element is constructed.games;capacity;scheduling;cooperation;allocation