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

Informationally Robust Equlibria

Informationally Robust Equilibria (IRE) are introduced in Robson (1994) as a refinement of Nash equilibria for e.g. bimatrix games, i.e. mixed extensions of two person finite games.Similar to the concept of perfect equilibria, basically the idea is that an IRE is a limit of some sequence of equilibria of perturbed games.Here, the perturbation has to do with the hypothetical possibility that the action of one the players is revealed to his fellow player before the fellow player has to decide on his own action.Whereas Robson models these perturbations in extensive form and uses subgame perfection to solve these games, we model the perturbations in strategic form, thus remaining in the class of bimatrix games. Moreover, within the perturbations we impose two possible types of tie breaking rules, which leads to the notions optimistic and pessimistic IRE.The paper provides motivation on IRE and its definition.Several properties will be discussed.In particular, we have that IRE is a strict concept, and that IRE components are faces of Nash components.Specific results from potential gamesnash equilibria;game theory;information

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

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

The consistency principle for set-valued solutions and a new direction for the theory of equilibrium refinements

game theory;equilibrium theory