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

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 Interval Games Arising from Airport Situations with Interval Data

This paper deals with the research area of cooperative interval games arising from airport situations with interval data. We also extend to airport interval games some results from classical theory.cooperative interval games;concave games;airport games;cost games;interval data

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

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

Operations Research Games: A Survey

This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved.Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players.This interplay between optimisation and allocation is the main subject of the area of operations research games.It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.cooperative games;operational research

On the Convexity of News Vendor Games

This study considers a simple newsvendor situation that consists of n retailers, all selling the same item with common purchasing costs and common selling prices.Groups of retailers might increase their expected joint profit by inventory centralization, which means that they make a joint order to satisfy total future demand.The resulting newsvendor games are shown to have non-empty cores in the literature.This study investigates convexity of newsvendor games.We focus our analysis on the class of newsvendor games with independent symmetric unimodal demand distributions after providing several examples outside this class that are not convex.Several interesting subclasses, containing convex games only, are identified.Additionally, we illustrate that these results can not be extended to all games in this class.game theory;inventory centralization;newsvendor;convexity

Proportionate Flow Shop Games

In a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines.By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face an additional problem: how to allocate the cost savings obtained by ordering the jobs optimally?In this paper, PFS games are defined as cooperative games associated to proportionate flow shop problems.It is seen that PFS games have a nonempty core.Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency.For this case an explicit expression for the Shapley value and a specific type of equal gain splitting rule which leads to core elements of the PFS game are proposed.Proportionate flow shop problems;core;convexity

On Iterated Dominance, Matrix Elimination, and Matched Paths

We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated weak dominance. The two-action case can be reformulated as a natural elimination problem on a matrix, the complexity of which turns out to be surprisingly difficult to characterize and ultimately remains open. We however establish connections to a matching problem along paths in a directed graph, which is computationally hard in general but can also be used to identify tractable cases of matrix elimination. We finally identify different classes of anonymous games where iterated dominance is in P and NP-complete, respectively.Comment: 12 pages, 3 figures, 27th International Symposium on Theoretical Aspects of Computer Science (STACS