On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

Allocation rules for hypergraph communication situations

This paper considers hypergraph communication situations, where for a group of agents the economic possibilities are described by a coalitional game and the communication possibilities are described by a hypergraph in which the nodes are the agents and the edges are the subgroups of agents who can effect communication. Axiomatic characterizations are provided for two allocation rules, the Myerson value and the position value.     

A note on theβ-measure for digraph competitions

Digraph games are cooperative TU-games associated to digraph competitions: domination structures that can be modeled by directed graphs. Examples come from sports competitions or from simple majority win digraphs corresponding to preference profiles for a group of individuals within the framework of social choice theory. Brink and Gilles (2000) defined theβ-measure of a digraph competition as the Shapley value of the corresponding digraph game. This paper provides a new characterization of theβ-measure.     

Source Apportionment for the Zinc—Containing Component of Air Particulate Matter using Automated Electron Probe Micro Analysis of Individual Particles

Abstract

A methodology is described for the apportionment of zinc-containing particulate matter sampled in the vicinity of a zinc smelter to their corresponding sources in the factory. Bulk samples of particulate matter from six potential emission sources were analysed by automated electron probe microanalysis (EPMA) in order to characterize the individual particles. Based on a data set of relative peak intensities and with the aid of a binary clustering method, the most important particle classes were identified. They were used as a basis for the development of a set of disjunct identification rules (decision rules), which were able to describe the classes in a unique manner. Applying these rules upon ambient particulate data enabled the estimation of relative contributions of different types of zinc-containing particles. Evidence was found that a large number of particles was modified by a soil component or by gas phase reactions.     

Measuring skill in games: several approaches discussed

An aspect of casino games that in general leads to discussions among both participants and spectators, is the relative extent to which a player can positively influence his results by making appropriate strategic choices. This question is closely related to the issue of how to distinguish between games of skill and games of chance. This is an issue that is interesting from a juridical point of view too, since in many countries the legitimacy of exploiting a specific game depends on the category to which it belongs. This paper summarizes recent developments concerning the measurement of skill in games. It points out the elements in the definitions that need closer attention, it illustrates the analysis with examples and it discusses further possibilities.     

Sequencing games with repeated players

Two classes of one machine sequencing situations are considered in which each job corresponds to exactly one player but a player may have more than one job to be processed, so called RP(repeated player) sequencing situations. In max-RP sequencing situations it is assumed that each player’s cost function is linear with respect to the maximum completion time of his jobs, whereas in min-RP sequencing situations the cost functions are linear with respect to the minimum completion times. For both classes, following explicit procedures to go from the initial processing order to an optimal order for the coalition of all players, equal gain splitting rules are defined. It is shown that these rules lead to core elements of the associated RP sequencing games. Moreover, it is seen that min-RP sequencing games are convex. We thank two referees for their valuable suggestions for improvement. Financial support for P. Calleja has been given by the Ministerio de Educación y Ciencia and FEDER under grant SEJ2005-02443/ECON, and by the Generalitat de Catalunya through a BE grant from AGAUR and grant 2005SGR00984.     

An Iterative Procedure for Evaluating Digraph Competitions

A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.