A characterization of a new value and an existing value for cooperative games with levels structure of cooperation

shapley value, banzhaf value, levels structure of cooperation

Human-Robot Collaboration as a new paradigm in circular economy for WEEE management

E-waste is a priority waste stream as identified by the European Commission due to fast technological changes and eagerness of consumers to acquire new products. The value chain of the Waste on Electric and Electronic Equipment (WEEE) has to face several challenges: the EU directives requesting collection targets for 2019–2022, the costs of disassembly processes which is highly dependent on the applied technology and type of discarded device, and the sale of the obtained components and/or raw materials, with market prices varying according to uncontrolled variables at world level. This paper presents a human-robot collaboration for a recycling process where tasks are opportunistically assigned to either a human-being or a robot depending on the condition of the discarded electronic device. This solution presents some important advantages; i.e. tedious and dangerous tasks are assigned to robots whereas more value-added tasks are allocated to humans, thus preserving jobs and increasing job satisfaction. Furthermore, first results from a prototype show greater productivity and profitable projected investment

Externalities and the nucleolus

In most economic applications, externalities prevail: the worth of a coalition depends on how the other players are organized. We show that there is a unique natural way of extending the nucleolus from (coalitional) games without externalities to games with externalities. This is in contrast to the Shapley value and the core for which many different extensions have been proposed

Collaborative Robots in e-waste Management

Nowadays manufacturing companies are going through an increasing public and government pressure to reduce the environmental impact of their operations. But when dealing with e-waste, some difficulties arise in classifying and dismantling electronic devices. Manual operations are financially prohibitive and full automation is also discarded due to the lack of uniformity of the disposed devices. A halfway solution is to let a human operator and a robot share the process. The goal of this research is the optimization of the recycling process of electronic equipments, applying both technical and economic criteria, and taking into account the latest developments in collaborative robots

Share Functions for Cooperative Games with Levels Structure of Cooperation

In a standard TU-game it is assumed that every subset of the player set can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered is the one of games with coalition structure. In such games the player set is partitioned into unions and players can only cooperate within their own union. Owen introduced a value for games with coalition structure under the assumption that also the unions can cooperate among them. Winter extended this value to games with levels structure of cooperation, which consists of a game and a finite sequence of partitions defined on the player set, each of them being coarser than the previous one. A share function for TU-games is a type of solution that assigns to every game a vector whose components add up to one, and thus they can be interpreted as players' shares in the worth to be allocated. Extending the approach to games with coalition structure developed by van den Brink and van der Laan (2005), we introduce a class of share functions for games with levels structure of cooperation by defining, for each player and each level, a standard TU-game. The share given to each player is then defined as the product of her shares in the games at every level. We show several desirable properties and provide axiomatic characterizations of this class of LS-share functions

Decomposing Dual Scale Soil Surface Roughness for Microwave Remote Sensing Applications

Soil surface roughness, as investigated in this study, is decomposed in a dual scale process. Therefore, we investigated photogrammetrically acquired roughness information over different agricultural fields in the size of 6-22 m(2) and decomposed them into a dual scale process by using geostatistical techniques. For the characterization of soil surface roughness, we calculated two different roughness indices (the RMS height s and the autocorrelation length l) differing significantly for each scale. While we could relate the small scale roughness pattern clearly to the seedbed rows, the larger second scale pattern could be related to the appearance of wheel tracks of the tillage machine used. As a result, major progress was made in the understanding of the different scales in soil surface roughness characterization and its quantification possibilities

From Hierarchies to Levels: New Solutions for Games with Hierarchical Structure

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict players ’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the structure relative to that player. To define each of these solutions, we consider a certain mapping that transforms any hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley Value to the class of games with levels structure. The transformations that map the set of hierarchical structures to the set of levels structures are also studied from an axiomatic viewpoint by means of properties that relate a player’s position in both types of structure